Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
St000277: Integer compositions ⟶ ℤ
Values
0 => [1] => 1
1 => [1] => 1
00 => [2] => 1
01 => [1,1] => 1
10 => [1,1] => 1
11 => [2] => 1
000 => [3] => 1
001 => [2,1] => 2
010 => [1,1,1] => 1
011 => [1,2] => 2
100 => [1,2] => 2
101 => [1,1,1] => 1
110 => [2,1] => 2
111 => [3] => 1
0000 => [4] => 1
0001 => [3,1] => 3
0010 => [2,1,1] => 3
0011 => [2,2] => 5
0100 => [1,1,2] => 3
0101 => [1,1,1,1] => 1
0110 => [1,2,1] => 5
0111 => [1,3] => 3
1000 => [1,3] => 3
1001 => [1,2,1] => 5
1010 => [1,1,1,1] => 1
1011 => [1,1,2] => 3
1100 => [2,2] => 5
1101 => [2,1,1] => 3
1110 => [3,1] => 3
1111 => [4] => 1
00000 => [5] => 1
00001 => [4,1] => 4
00010 => [3,1,1] => 6
00011 => [3,2] => 9
00100 => [2,1,2] => 11
00101 => [2,1,1,1] => 4
00110 => [2,2,1] => 16
00111 => [2,3] => 9
01000 => [1,1,3] => 6
01001 => [1,1,2,1] => 9
01010 => [1,1,1,1,1] => 1
01011 => [1,1,1,2] => 4
01100 => [1,2,2] => 16
01101 => [1,2,1,1] => 9
01110 => [1,3,1] => 11
01111 => [1,4] => 4
10000 => [1,4] => 4
10001 => [1,3,1] => 11
10010 => [1,2,1,1] => 9
10011 => [1,2,2] => 16
10100 => [1,1,1,2] => 4
10101 => [1,1,1,1,1] => 1
10110 => [1,1,2,1] => 9
10111 => [1,1,3] => 6
11000 => [2,3] => 9
11001 => [2,2,1] => 16
11010 => [2,1,1,1] => 4
11011 => [2,1,2] => 11
11100 => [3,2] => 9
11101 => [3,1,1] => 6
11110 => [4,1] => 4
11111 => [5] => 1
000000 => [6] => 1
000001 => [5,1] => 5
000010 => [4,1,1] => 10
000011 => [4,2] => 14
000100 => [3,1,2] => 26
000101 => [3,1,1,1] => 10
000110 => [3,2,1] => 35
000111 => [3,3] => 19
001000 => [2,1,3] => 26
001001 => [2,1,2,1] => 40
001010 => [2,1,1,1,1] => 5
001011 => [2,1,1,2] => 19
001100 => [2,2,2] => 61
001101 => [2,2,1,1] => 35
001110 => [2,3,1] => 40
001111 => [2,4] => 14
010000 => [1,1,4] => 10
010001 => [1,1,3,1] => 26
010010 => [1,1,2,1,1] => 19
010011 => [1,1,2,2] => 35
010100 => [1,1,1,1,2] => 5
010101 => [1,1,1,1,1,1] => 1
010110 => [1,1,1,2,1] => 14
010111 => [1,1,1,3] => 10
011000 => [1,2,3] => 35
011001 => [1,2,2,1] => 61
011010 => [1,2,1,1,1] => 14
011011 => [1,2,1,2] => 40
011100 => [1,3,2] => 40
011101 => [1,3,1,1] => 26
011110 => [1,4,1] => 19
011111 => [1,5] => 5
100000 => [1,5] => 5
100001 => [1,4,1] => 19
100010 => [1,3,1,1] => 26
100011 => [1,3,2] => 40
100100 => [1,2,1,2] => 40
100101 => [1,2,1,1,1] => 14
100110 => [1,2,2,1] => 61
>>> Load all 1345 entries. <<<100111 => [1,2,3] => 35
101000 => [1,1,1,3] => 10
101001 => [1,1,1,2,1] => 14
101010 => [1,1,1,1,1,1] => 1
101011 => [1,1,1,1,2] => 5
101100 => [1,1,2,2] => 35
101101 => [1,1,2,1,1] => 19
101110 => [1,1,3,1] => 26
101111 => [1,1,4] => 10
110000 => [2,4] => 14
110001 => [2,3,1] => 40
110010 => [2,2,1,1] => 35
110011 => [2,2,2] => 61
110100 => [2,1,1,2] => 19
110101 => [2,1,1,1,1] => 5
110110 => [2,1,2,1] => 40
110111 => [2,1,3] => 26
111000 => [3,3] => 19
111001 => [3,2,1] => 35
111010 => [3,1,1,1] => 10
111011 => [3,1,2] => 26
111100 => [4,2] => 14
111101 => [4,1,1] => 10
111110 => [5,1] => 5
111111 => [6] => 1
0000000 => [7] => 1
0000001 => [6,1] => 6
0000010 => [5,1,1] => 15
0000011 => [5,2] => 20
0000100 => [4,1,2] => 50
0000101 => [4,1,1,1] => 20
0000110 => [4,2,1] => 64
0000111 => [4,3] => 34
0001000 => [3,1,3] => 71
0001001 => [3,1,2,1] => 111
0001010 => [3,1,1,1,1] => 15
0001011 => [3,1,1,2] => 55
0001100 => [3,2,2] => 155
0001101 => [3,2,1,1] => 90
0001110 => [3,3,1] => 99
0001111 => [3,4] => 34
0010000 => [2,1,4] => 50
0010001 => [2,1,3,1] => 132
0010010 => [2,1,2,1,1] => 99
0010011 => [2,1,2,2] => 181
0010100 => [2,1,1,1,2] => 29
0010101 => [2,1,1,1,1,1] => 6
0010110 => [2,1,1,2,1] => 78
0010111 => [2,1,1,3] => 55
0011000 => [2,2,3] => 155
0011001 => [2,2,2,1] => 272
0011010 => [2,2,1,1,1] => 64
0011011 => [2,2,1,2] => 181
0011100 => [2,3,2] => 169
0011101 => [2,3,1,1] => 111
0011110 => [2,4,1] => 78
0011111 => [2,5] => 20
0100000 => [1,1,5] => 15
0100001 => [1,1,4,1] => 55
0100010 => [1,1,3,1,1] => 71
0100011 => [1,1,3,2] => 111
0100100 => [1,1,2,1,2] => 99
0100101 => [1,1,2,1,1,1] => 34
0100110 => [1,1,2,2,1] => 155
0100111 => [1,1,2,3] => 90
0101000 => [1,1,1,1,3] => 15
0101001 => [1,1,1,1,2,1] => 20
0101010 => [1,1,1,1,1,1,1] => 1
0101011 => [1,1,1,1,1,2] => 6
0101100 => [1,1,1,2,2] => 64
0101101 => [1,1,1,2,1,1] => 34
0101110 => [1,1,1,3,1] => 50
0101111 => [1,1,1,4] => 20
0110000 => [1,2,4] => 64
0110001 => [1,2,3,1] => 181
0110010 => [1,2,2,1,1] => 155
0110011 => [1,2,2,2] => 272
0110100 => [1,2,1,1,2] => 78
0110101 => [1,2,1,1,1,1] => 20
0110110 => [1,2,1,2,1] => 169
0110111 => [1,2,1,3] => 111
0111000 => [1,3,3] => 99
0111001 => [1,3,2,1] => 181
0111010 => [1,3,1,1,1] => 50
0111011 => [1,3,1,2] => 132
0111100 => [1,4,2] => 78
0111101 => [1,4,1,1] => 55
0111110 => [1,5,1] => 29
0111111 => [1,6] => 6
1000000 => [1,6] => 6
1000001 => [1,5,1] => 29
1000010 => [1,4,1,1] => 55
1000011 => [1,4,2] => 78
1000100 => [1,3,1,2] => 132
1000101 => [1,3,1,1,1] => 50
1000110 => [1,3,2,1] => 181
1000111 => [1,3,3] => 99
1001000 => [1,2,1,3] => 111
1001001 => [1,2,1,2,1] => 169
1001010 => [1,2,1,1,1,1] => 20
1001011 => [1,2,1,1,2] => 78
1001100 => [1,2,2,2] => 272
1001101 => [1,2,2,1,1] => 155
1001110 => [1,2,3,1] => 181
1001111 => [1,2,4] => 64
1010000 => [1,1,1,4] => 20
1010001 => [1,1,1,3,1] => 50
1010010 => [1,1,1,2,1,1] => 34
1010011 => [1,1,1,2,2] => 64
1010100 => [1,1,1,1,1,2] => 6
1010101 => [1,1,1,1,1,1,1] => 1
1010110 => [1,1,1,1,2,1] => 20
1010111 => [1,1,1,1,3] => 15
1011000 => [1,1,2,3] => 90
1011001 => [1,1,2,2,1] => 155
1011010 => [1,1,2,1,1,1] => 34
1011011 => [1,1,2,1,2] => 99
1011100 => [1,1,3,2] => 111
1011101 => [1,1,3,1,1] => 71
1011110 => [1,1,4,1] => 55
1011111 => [1,1,5] => 15
1100000 => [2,5] => 20
1100001 => [2,4,1] => 78
1100010 => [2,3,1,1] => 111
1100011 => [2,3,2] => 169
1100100 => [2,2,1,2] => 181
1100101 => [2,2,1,1,1] => 64
1100110 => [2,2,2,1] => 272
1100111 => [2,2,3] => 155
1101000 => [2,1,1,3] => 55
1101001 => [2,1,1,2,1] => 78
1101010 => [2,1,1,1,1,1] => 6
1101011 => [2,1,1,1,2] => 29
1101100 => [2,1,2,2] => 181
1101101 => [2,1,2,1,1] => 99
1101110 => [2,1,3,1] => 132
1101111 => [2,1,4] => 50
1110000 => [3,4] => 34
1110001 => [3,3,1] => 99
1110010 => [3,2,1,1] => 90
1110011 => [3,2,2] => 155
1110100 => [3,1,1,2] => 55
1110101 => [3,1,1,1,1] => 15
1110110 => [3,1,2,1] => 111
1110111 => [3,1,3] => 71
1111000 => [4,3] => 34
1111001 => [4,2,1] => 64
1111010 => [4,1,1,1] => 20
1111011 => [4,1,2] => 50
1111100 => [5,2] => 20
1111101 => [5,1,1] => 15
1111110 => [6,1] => 6
1111111 => [7] => 1
00000000 => [8] => 1
00000001 => [7,1] => 7
00000010 => [6,1,1] => 21
00000011 => [6,2] => 27
00000100 => [5,1,2] => 85
00000101 => [5,1,1,1] => 35
00000110 => [5,2,1] => 105
00000111 => [5,3] => 55
00001000 => [4,1,3] => 155
00001001 => [4,1,2,1] => 245
00001010 => [4,1,1,1,1] => 35
00001011 => [4,1,1,2] => 125
00001100 => [4,2,2] => 323
00001101 => [4,2,1,1] => 189
00001110 => [4,3,1] => 203
00001111 => [4,4] => 69
00010000 => [3,1,4] => 155
00010001 => [3,1,3,1] => 413
00010010 => [3,1,2,1,1] => 315
00010011 => [3,1,2,2] => 573
00010100 => [3,1,1,1,2] => 99
00010101 => [3,1,1,1,1,1] => 21
00010110 => [3,1,1,2,1] => 259
00010111 => [3,1,1,3] => 181
00011000 => [3,2,3] => 449
00011001 => [3,2,2,1] => 791
00011010 => [3,2,1,1,1] => 189
00011011 => [3,2,1,2] => 531
00011100 => [3,3,2] => 477
00011101 => [3,3,1,1] => 315
00011110 => [3,4,1] => 217
00011111 => [3,5] => 55
00100000 => [2,1,5] => 85
00100001 => [2,1,4,1] => 315
00100010 => [2,1,3,1,1] => 413
00100011 => [2,1,3,2] => 643
00100100 => [2,1,2,1,2] => 589
00100101 => [2,1,2,1,1,1] => 203
00100110 => [2,1,2,2,1] => 917
00100111 => [2,1,2,3] => 531
00101000 => [2,1,1,1,3] => 99
00101001 => [2,1,1,1,2,1] => 133
00101010 => [2,1,1,1,1,1,1] => 7
00101011 => [2,1,1,1,1,2] => 41
00101100 => [2,1,1,2,2] => 407
00101101 => [2,1,1,2,1,1] => 217
00101110 => [2,1,1,3,1] => 315
00101111 => [2,1,1,4] => 125
00110000 => [2,2,4] => 323
00110001 => [2,2,3,1] => 917
00110010 => [2,2,2,1,1] => 791
00110011 => [2,2,2,2] => 1385
00110100 => [2,2,1,1,2] => 407
00110101 => [2,2,1,1,1,1] => 105
00110110 => [2,2,1,2,1] => 875
00110111 => [2,2,1,3] => 573
00111000 => [2,3,3] => 477
00111001 => [2,3,2,1] => 875
00111010 => [2,3,1,1,1] => 245
00111011 => [2,3,1,2] => 643
00111100 => [2,4,2] => 365
00111101 => [2,4,1,1] => 259
00111110 => [2,5,1] => 133
00111111 => [2,6] => 27
01000000 => [1,1,6] => 21
01000001 => [1,1,5,1] => 99
01000010 => [1,1,4,1,1] => 181
01000011 => [1,1,4,2] => 259
01000100 => [1,1,3,1,2] => 413
01000101 => [1,1,3,1,1,1] => 155
01000110 => [1,1,3,2,1] => 573
01000111 => [1,1,3,3] => 315
01001000 => [1,1,2,1,3] => 315
01001001 => [1,1,2,1,2,1] => 477
01001010 => [1,1,2,1,1,1,1] => 55
01001011 => [1,1,2,1,1,2] => 217
01001100 => [1,1,2,2,2] => 791
01001101 => [1,1,2,2,1,1] => 449
01001110 => [1,1,2,3,1] => 531
01001111 => [1,1,2,4] => 189
01010000 => [1,1,1,1,4] => 35
01010001 => [1,1,1,1,3,1] => 85
01010010 => [1,1,1,1,2,1,1] => 55
01010011 => [1,1,1,1,2,2] => 105
01010100 => [1,1,1,1,1,1,2] => 7
01010101 => [1,1,1,1,1,1,1,1] => 1
01010110 => [1,1,1,1,1,2,1] => 27
01010111 => [1,1,1,1,1,3] => 21
01011000 => [1,1,1,2,3] => 189
01011001 => [1,1,1,2,2,1] => 323
01011010 => [1,1,1,2,1,1,1] => 69
01011011 => [1,1,1,2,1,2] => 203
01011100 => [1,1,1,3,2] => 245
01011101 => [1,1,1,3,1,1] => 155
01011110 => [1,1,1,4,1] => 125
01011111 => [1,1,1,5] => 35
01100000 => [1,2,5] => 105
01100001 => [1,2,4,1] => 407
01100010 => [1,2,3,1,1] => 573
01100011 => [1,2,3,2] => 875
01100100 => [1,2,2,1,2] => 917
01100101 => [1,2,2,1,1,1] => 323
01100110 => [1,2,2,2,1] => 1385
01100111 => [1,2,2,3] => 791
01101000 => [1,2,1,1,3] => 259
01101001 => [1,2,1,1,2,1] => 365
01101010 => [1,2,1,1,1,1,1] => 27
01101011 => [1,2,1,1,1,2] => 133
01101100 => [1,2,1,2,2] => 875
01101101 => [1,2,1,2,1,1] => 477
01101110 => [1,2,1,3,1] => 643
01101111 => [1,2,1,4] => 245
01110000 => [1,3,4] => 203
01110001 => [1,3,3,1] => 589
01110010 => [1,3,2,1,1] => 531
01110011 => [1,3,2,2] => 917
01110100 => [1,3,1,1,2] => 315
01110101 => [1,3,1,1,1,1] => 85
01110110 => [1,3,1,2,1] => 643
01110111 => [1,3,1,3] => 413
01111000 => [1,4,3] => 217
01111001 => [1,4,2,1] => 407
01111010 => [1,4,1,1,1] => 125
01111011 => [1,4,1,2] => 315
01111100 => [1,5,2] => 133
01111101 => [1,5,1,1] => 99
01111110 => [1,6,1] => 41
01111111 => [1,7] => 7
10000000 => [1,7] => 7
10000001 => [1,6,1] => 41
10000010 => [1,5,1,1] => 99
10000011 => [1,5,2] => 133
10000100 => [1,4,1,2] => 315
10000101 => [1,4,1,1,1] => 125
10000110 => [1,4,2,1] => 407
10000111 => [1,4,3] => 217
10001000 => [1,3,1,3] => 413
10001001 => [1,3,1,2,1] => 643
10001010 => [1,3,1,1,1,1] => 85
10001011 => [1,3,1,1,2] => 315
10001100 => [1,3,2,2] => 917
10001101 => [1,3,2,1,1] => 531
10001110 => [1,3,3,1] => 589
10001111 => [1,3,4] => 203
10010000 => [1,2,1,4] => 245
10010001 => [1,2,1,3,1] => 643
10010010 => [1,2,1,2,1,1] => 477
10010011 => [1,2,1,2,2] => 875
10010100 => [1,2,1,1,1,2] => 133
10010101 => [1,2,1,1,1,1,1] => 27
10010110 => [1,2,1,1,2,1] => 365
10010111 => [1,2,1,1,3] => 259
10011000 => [1,2,2,3] => 791
10011001 => [1,2,2,2,1] => 1385
10011010 => [1,2,2,1,1,1] => 323
10011011 => [1,2,2,1,2] => 917
10011100 => [1,2,3,2] => 875
10011101 => [1,2,3,1,1] => 573
10011110 => [1,2,4,1] => 407
10011111 => [1,2,5] => 105
10100000 => [1,1,1,5] => 35
10100001 => [1,1,1,4,1] => 125
10100010 => [1,1,1,3,1,1] => 155
10100011 => [1,1,1,3,2] => 245
10100100 => [1,1,1,2,1,2] => 203
10100101 => [1,1,1,2,1,1,1] => 69
10100110 => [1,1,1,2,2,1] => 323
10100111 => [1,1,1,2,3] => 189
10101000 => [1,1,1,1,1,3] => 21
10101001 => [1,1,1,1,1,2,1] => 27
10101010 => [1,1,1,1,1,1,1,1] => 1
10101011 => [1,1,1,1,1,1,2] => 7
10101100 => [1,1,1,1,2,2] => 105
10101101 => [1,1,1,1,2,1,1] => 55
10101110 => [1,1,1,1,3,1] => 85
10101111 => [1,1,1,1,4] => 35
10110000 => [1,1,2,4] => 189
10110001 => [1,1,2,3,1] => 531
10110010 => [1,1,2,2,1,1] => 449
10110011 => [1,1,2,2,2] => 791
10110100 => [1,1,2,1,1,2] => 217
10110101 => [1,1,2,1,1,1,1] => 55
10110110 => [1,1,2,1,2,1] => 477
10110111 => [1,1,2,1,3] => 315
10111000 => [1,1,3,3] => 315
10111001 => [1,1,3,2,1] => 573
10111010 => [1,1,3,1,1,1] => 155
10111011 => [1,1,3,1,2] => 413
10111100 => [1,1,4,2] => 259
10111101 => [1,1,4,1,1] => 181
10111110 => [1,1,5,1] => 99
10111111 => [1,1,6] => 21
11000000 => [2,6] => 27
11000001 => [2,5,1] => 133
11000010 => [2,4,1,1] => 259
11000011 => [2,4,2] => 365
11000100 => [2,3,1,2] => 643
11000101 => [2,3,1,1,1] => 245
11000110 => [2,3,2,1] => 875
11000111 => [2,3,3] => 477
11001000 => [2,2,1,3] => 573
11001001 => [2,2,1,2,1] => 875
11001010 => [2,2,1,1,1,1] => 105
11001011 => [2,2,1,1,2] => 407
11001100 => [2,2,2,2] => 1385
11001101 => [2,2,2,1,1] => 791
11001110 => [2,2,3,1] => 917
11001111 => [2,2,4] => 323
11010000 => [2,1,1,4] => 125
11010001 => [2,1,1,3,1] => 315
11010010 => [2,1,1,2,1,1] => 217
11010011 => [2,1,1,2,2] => 407
11010100 => [2,1,1,1,1,2] => 41
11010101 => [2,1,1,1,1,1,1] => 7
11010110 => [2,1,1,1,2,1] => 133
11010111 => [2,1,1,1,3] => 99
11011000 => [2,1,2,3] => 531
11011001 => [2,1,2,2,1] => 917
11011010 => [2,1,2,1,1,1] => 203
11011011 => [2,1,2,1,2] => 589
11011100 => [2,1,3,2] => 643
11011101 => [2,1,3,1,1] => 413
11011110 => [2,1,4,1] => 315
11011111 => [2,1,5] => 85
11100000 => [3,5] => 55
11100001 => [3,4,1] => 217
11100010 => [3,3,1,1] => 315
11100011 => [3,3,2] => 477
11100100 => [3,2,1,2] => 531
11100101 => [3,2,1,1,1] => 189
11100110 => [3,2,2,1] => 791
11100111 => [3,2,3] => 449
11101000 => [3,1,1,3] => 181
11101001 => [3,1,1,2,1] => 259
11101010 => [3,1,1,1,1,1] => 21
11101011 => [3,1,1,1,2] => 99
11101100 => [3,1,2,2] => 573
11101101 => [3,1,2,1,1] => 315
11101110 => [3,1,3,1] => 413
11101111 => [3,1,4] => 155
11110000 => [4,4] => 69
11110001 => [4,3,1] => 203
11110010 => [4,2,1,1] => 189
11110011 => [4,2,2] => 323
11110100 => [4,1,1,2] => 125
11110101 => [4,1,1,1,1] => 35
11110110 => [4,1,2,1] => 245
11110111 => [4,1,3] => 155
11111000 => [5,3] => 55
11111001 => [5,2,1] => 105
11111010 => [5,1,1,1] => 35
11111011 => [5,1,2] => 85
11111100 => [6,2] => 27
11111101 => [6,1,1] => 21
11111110 => [7,1] => 7
11111111 => [8] => 1
000000000 => [9] => 1
000000001 => [8,1] => 8
000000010 => [7,1,1] => 28
000000011 => [7,2] => 35
000000100 => [6,1,2] => 133
000000101 => [6,1,1,1] => 56
000000110 => [6,2,1] => 160
000000111 => [6,3] => 83
000001000 => [5,1,3] => 295
000001001 => [5,1,2,1] => 470
000001010 => [5,1,1,1,1] => 70
000001011 => [5,1,1,2] => 245
000001100 => [5,2,2] => 595
000001101 => [5,2,1,1] => 350
000001110 => [5,3,1] => 370
000001111 => [5,4] => 125
000010000 => [4,1,4] => 379
000010001 => [4,1,3,1] => 1016
000010010 => [4,1,2,1,1] => 784
000010011 => [4,1,2,2] => 1421
000010100 => [4,1,1,1,2] => 259
000010101 => [4,1,1,1,1,1] => 56
000010110 => [4,1,1,2,1] => 664
000010111 => [4,1,1,3] => 461
000011000 => [4,2,3] => 1051
000011001 => [4,2,2,1] => 1856
000011010 => [4,2,1,1,1] => 448
000011011 => [4,2,1,2] => 1253
000011100 => [4,3,2] => 1099
000011101 => [4,3,1,1] => 728
000011110 => [4,4,1] => 496
000011111 => [4,5] => 125
000100000 => [3,1,5] => 295
000100001 => [3,1,4,1] => 1100
000100010 => [3,1,3,1,1] => 1456
000100011 => [3,1,3,2] => 2261
000100100 => [3,1,2,1,2] => 2107
000100101 => [3,1,2,1,1,1] => 728
000100110 => [3,1,2,2,1] => 3268
000100111 => [3,1,2,3] => 1889
000101000 => [3,1,1,1,3] => 379
000101001 => [3,1,1,1,2,1] => 512
000101010 => [3,1,1,1,1,1,1] => 28
000101011 => [3,1,1,1,1,2] => 161
000101100 => [3,1,1,2,2] => 1519
000101101 => [3,1,1,2,1,1] => 812
000101110 => [3,1,1,3,1] => 1168
000101111 => [3,1,1,4] => 461
000110000 => [3,2,4] => 1051
000110001 => [3,2,3,1] => 2990
000110010 => [3,2,2,1,1] => 2590
000110011 => [3,2,2,2] => 4529
000110100 => [3,2,1,1,2] => 1351
000110101 => [3,2,1,1,1,1] => 350
000110110 => [3,2,1,2,1] => 2890
000110111 => [3,2,1,3] => 1889
000111000 => [3,3,3] => 1513
000111001 => [3,3,2,1] => 2780
000111010 => [3,3,1,1,1] => 784
000111011 => [3,3,1,2] => 2051
000111100 => [3,4,2] => 1141
000111101 => [3,4,1,1] => 812
000111110 => [3,5,1] => 412
000111111 => [3,6] => 83
001000000 => [2,1,6] => 133
001000001 => [2,1,5,1] => 632
001000010 => [2,1,4,1,1] => 1168
001000011 => [2,1,4,2] => 1667
001000100 => [2,1,3,1,2] => 2701
001000101 => [2,1,3,1,1,1] => 1016
001000110 => [2,1,3,2,1] => 3736
001000111 => [2,1,3,3] => 2051
001001000 => [2,1,2,1,3] => 2107
001001001 => [2,1,2,1,2,1] => 3194
001001010 => [2,1,2,1,1,1,1] => 370
001001011 => [2,1,2,1,1,2] => 1457
001001100 => [2,1,2,2,2] => 5263
001001101 => [2,1,2,2,1,1] => 2990
001001110 => [2,1,2,3,1] => 3526
001001111 => [2,1,2,4] => 1253
001010000 => [2,1,1,1,4] => 259
001010001 => [2,1,1,1,3,1] => 632
001010010 => [2,1,1,1,2,1,1] => 412
001010011 => [2,1,1,1,2,2] => 785
001010100 => [2,1,1,1,1,1,2] => 55
001010101 => [2,1,1,1,1,1,1,1] => 8
001010110 => [2,1,1,1,1,2,1] => 208
001010111 => [2,1,1,1,1,3] => 161
001011000 => [2,1,1,2,3] => 1351
001011001 => [2,1,1,2,2,1] => 2312
001011010 => [2,1,1,2,1,1,1] => 496
001011011 => [2,1,1,2,1,2] => 1457
001011100 => [2,1,1,3,2] => 1735
001011101 => [2,1,1,3,1,1] => 1100
001011110 => [2,1,1,4,1] => 880
001011111 => [2,1,1,5] => 245
001100000 => [2,2,5] => 595
001100001 => [2,2,4,1] => 2312
001100010 => [2,2,3,1,1] => 3268
001100011 => [2,2,3,2] => 4985
001100100 => [2,2,2,1,2] => 5263
001100101 => [2,2,2,1,1,1] => 1856
001100110 => [2,2,2,2,1] => 7936
001100111 => [2,2,2,3] => 4529
001101000 => [2,2,1,1,3] => 1519
001101001 => [2,2,1,1,2,1] => 2144
001101010 => [2,2,1,1,1,1,1] => 160
001101011 => [2,2,1,1,1,2] => 785
001101100 => [2,2,1,2,2] => 5095
001101101 => [2,2,1,2,1,1] => 2780
001101110 => [2,2,1,3,1] => 3736
001101111 => [2,2,1,4] => 1421
001110000 => [2,3,4] => 1099
001110001 => [2,3,3,1] => 3194
001110010 => [2,3,2,1,1] => 2890
001110011 => [2,3,2,2] => 4985
001110100 => [2,3,1,1,2] => 1735
001110101 => [2,3,1,1,1,1] => 470
001110110 => [2,3,1,2,1] => 3526
001110111 => [2,3,1,3] => 2261
001111000 => [2,4,3] => 1141
001111001 => [2,4,2,1] => 2144
001111010 => [2,4,1,1,1] => 664
001111011 => [2,4,1,2] => 1667
001111100 => [2,5,2] => 685
001111101 => [2,5,1,1] => 512
001111110 => [2,6,1] => 208
001111111 => [2,7] => 35
010000000 => [1,1,7] => 28
010000001 => [1,1,6,1] => 161
010000010 => [1,1,5,1,1] => 379
010000011 => [1,1,5,2] => 512
010000100 => [1,1,4,1,2] => 1168
010000101 => [1,1,4,1,1,1] => 461
010000110 => [1,1,4,2,1] => 1519
010000111 => [1,1,4,3] => 812
010001000 => [1,1,3,1,3] => 1456
010001001 => [1,1,3,1,2,1] => 2261
010001010 => [1,1,3,1,1,1,1] => 295
010001011 => [1,1,3,1,1,2] => 1100
010001100 => [1,1,3,2,2] => 3268
010001101 => [1,1,3,2,1,1] => 1889
010001110 => [1,1,3,3,1] => 2107
010001111 => [1,1,3,4] => 728
010010000 => [1,1,2,1,4] => 784
010010001 => [1,1,2,1,3,1] => 2051
010010010 => [1,1,2,1,2,1,1] => 1513
010010011 => [1,1,2,1,2,2] => 2780
010010100 => [1,1,2,1,1,1,2] => 412
010010101 => [1,1,2,1,1,1,1,1] => 83
010010110 => [1,1,2,1,1,2,1] => 1141
010010111 => [1,1,2,1,1,3] => 812
010011000 => [1,1,2,2,3] => 2590
010011001 => [1,1,2,2,2,1] => 4529
010011010 => [1,1,2,2,1,1,1] => 1051
010011011 => [1,1,2,2,1,2] => 2990
010011100 => [1,1,2,3,2] => 2890
010011101 => [1,1,2,3,1,1] => 1889
010011110 => [1,1,2,4,1] => 1351
010011111 => [1,1,2,5] => 350
010100000 => [1,1,1,1,5] => 70
010100001 => [1,1,1,1,4,1] => 245
010100010 => [1,1,1,1,3,1,1] => 295
010100011 => [1,1,1,1,3,2] => 470
010100100 => [1,1,1,1,2,1,2] => 370
010100101 => [1,1,1,1,2,1,1,1] => 125
010100110 => [1,1,1,1,2,2,1] => 595
010100111 => [1,1,1,1,2,3] => 350
010101000 => [1,1,1,1,1,1,3] => 28
010101001 => [1,1,1,1,1,1,2,1] => 35
010101010 => [1,1,1,1,1,1,1,1,1] => 1
010101011 => [1,1,1,1,1,1,1,2] => 8
010101100 => [1,1,1,1,1,2,2] => 160
010101101 => [1,1,1,1,1,2,1,1] => 83
010101110 => [1,1,1,1,1,3,1] => 133
010101111 => [1,1,1,1,1,4] => 56
010110000 => [1,1,1,2,4] => 448
010110001 => [1,1,1,2,3,1] => 1253
010110010 => [1,1,1,2,2,1,1] => 1051
010110011 => [1,1,1,2,2,2] => 1856
010110100 => [1,1,1,2,1,1,2] => 496
010110101 => [1,1,1,2,1,1,1,1] => 125
010110110 => [1,1,1,2,1,2,1] => 1099
010110111 => [1,1,1,2,1,3] => 728
010111000 => [1,1,1,3,3] => 784
010111001 => [1,1,1,3,2,1] => 1421
010111010 => [1,1,1,3,1,1,1] => 379
010111011 => [1,1,1,3,1,2] => 1016
010111100 => [1,1,1,4,2] => 664
010111101 => [1,1,1,4,1,1] => 461
010111110 => [1,1,1,5,1] => 259
010111111 => [1,1,1,6] => 56
011000000 => [1,2,6] => 160
011000001 => [1,2,5,1] => 785
011000010 => [1,2,4,1,1] => 1519
011000011 => [1,2,4,2] => 2144
011000100 => [1,2,3,1,2] => 3736
011000101 => [1,2,3,1,1,1] => 1421
011000110 => [1,2,3,2,1] => 5095
011000111 => [1,2,3,3] => 2780
011001000 => [1,2,2,1,3] => 3268
011001001 => [1,2,2,1,2,1] => 4985
011001010 => [1,2,2,1,1,1,1] => 595
011001011 => [1,2,2,1,1,2] => 2312
011001100 => [1,2,2,2,2] => 7936
011001101 => [1,2,2,2,1,1] => 4529
011001110 => [1,2,2,3,1] => 5263
011001111 => [1,2,2,4] => 1856
011010000 => [1,2,1,1,4] => 664
011010001 => [1,2,1,1,3,1] => 1667
011010010 => [1,2,1,1,2,1,1] => 1141
011010011 => [1,2,1,1,2,2] => 2144
011010100 => [1,2,1,1,1,1,2] => 208
011010101 => [1,2,1,1,1,1,1,1] => 35
011010110 => [1,2,1,1,1,2,1] => 685
011010111 => [1,2,1,1,1,3] => 512
011011000 => [1,2,1,2,3] => 2890
011011001 => [1,2,1,2,2,1] => 4985
011011010 => [1,2,1,2,1,1,1] => 1099
011011011 => [1,2,1,2,1,2] => 3194
011011100 => [1,2,1,3,2] => 3526
011011101 => [1,2,1,3,1,1] => 2261
011011110 => [1,2,1,4,1] => 1735
011011111 => [1,2,1,5] => 470
011100000 => [1,3,5] => 370
011100001 => [1,3,4,1] => 1457
011100010 => [1,3,3,1,1] => 2107
011100011 => [1,3,3,2] => 3194
011100100 => [1,3,2,1,2] => 3526
011100101 => [1,3,2,1,1,1] => 1253
011100110 => [1,3,2,2,1] => 5263
011100111 => [1,3,2,3] => 2990
011101000 => [1,3,1,1,3] => 1168
011101001 => [1,3,1,1,2,1] => 1667
011101010 => [1,3,1,1,1,1,1] => 133
011101011 => [1,3,1,1,1,2] => 632
011101100 => [1,3,1,2,2] => 3736
011101101 => [1,3,1,2,1,1] => 2051
011101110 => [1,3,1,3,1] => 2701
011101111 => [1,3,1,4] => 1016
011110000 => [1,4,4] => 496
011110001 => [1,4,3,1] => 1457
011110010 => [1,4,2,1,1] => 1351
011110011 => [1,4,2,2] => 2312
011110100 => [1,4,1,1,2] => 880
011110101 => [1,4,1,1,1,1] => 245
011110110 => [1,4,1,2,1] => 1735
011110111 => [1,4,1,3] => 1100
011111000 => [1,5,3] => 412
011111001 => [1,5,2,1] => 785
011111010 => [1,5,1,1,1] => 259
011111011 => [1,5,1,2] => 632
011111100 => [1,6,2] => 208
011111101 => [1,6,1,1] => 161
011111110 => [1,7,1] => 55
011111111 => [1,8] => 8
100000000 => [1,8] => 8
100000001 => [1,7,1] => 55
100000010 => [1,6,1,1] => 161
100000011 => [1,6,2] => 208
100000100 => [1,5,1,2] => 632
100000101 => [1,5,1,1,1] => 259
100000110 => [1,5,2,1] => 785
100000111 => [1,5,3] => 412
100001000 => [1,4,1,3] => 1100
100001001 => [1,4,1,2,1] => 1735
100001010 => [1,4,1,1,1,1] => 245
100001011 => [1,4,1,1,2] => 880
100001100 => [1,4,2,2] => 2312
100001101 => [1,4,2,1,1] => 1351
100001110 => [1,4,3,1] => 1457
100001111 => [1,4,4] => 496
100010000 => [1,3,1,4] => 1016
100010001 => [1,3,1,3,1] => 2701
100010010 => [1,3,1,2,1,1] => 2051
100010011 => [1,3,1,2,2] => 3736
100010100 => [1,3,1,1,1,2] => 632
100010101 => [1,3,1,1,1,1,1] => 133
100010110 => [1,3,1,1,2,1] => 1667
100010111 => [1,3,1,1,3] => 1168
100011000 => [1,3,2,3] => 2990
100011001 => [1,3,2,2,1] => 5263
100011010 => [1,3,2,1,1,1] => 1253
100011011 => [1,3,2,1,2] => 3526
100011100 => [1,3,3,2] => 3194
100011101 => [1,3,3,1,1] => 2107
100011110 => [1,3,4,1] => 1457
100011111 => [1,3,5] => 370
100100000 => [1,2,1,5] => 470
100100001 => [1,2,1,4,1] => 1735
100100010 => [1,2,1,3,1,1] => 2261
100100011 => [1,2,1,3,2] => 3526
100100100 => [1,2,1,2,1,2] => 3194
100100101 => [1,2,1,2,1,1,1] => 1099
100100110 => [1,2,1,2,2,1] => 4985
100100111 => [1,2,1,2,3] => 2890
100101000 => [1,2,1,1,1,3] => 512
100101001 => [1,2,1,1,1,2,1] => 685
100101010 => [1,2,1,1,1,1,1,1] => 35
100101011 => [1,2,1,1,1,1,2] => 208
100101100 => [1,2,1,1,2,2] => 2144
100101101 => [1,2,1,1,2,1,1] => 1141
100101110 => [1,2,1,1,3,1] => 1667
100101111 => [1,2,1,1,4] => 664
100110000 => [1,2,2,4] => 1856
100110001 => [1,2,2,3,1] => 5263
100110010 => [1,2,2,2,1,1] => 4529
100110011 => [1,2,2,2,2] => 7936
100110100 => [1,2,2,1,1,2] => 2312
100110101 => [1,2,2,1,1,1,1] => 595
100110110 => [1,2,2,1,2,1] => 4985
100110111 => [1,2,2,1,3] => 3268
100111000 => [1,2,3,3] => 2780
100111001 => [1,2,3,2,1] => 5095
100111010 => [1,2,3,1,1,1] => 1421
100111011 => [1,2,3,1,2] => 3736
100111100 => [1,2,4,2] => 2144
100111101 => [1,2,4,1,1] => 1519
100111110 => [1,2,5,1] => 785
100111111 => [1,2,6] => 160
101000000 => [1,1,1,6] => 56
101000001 => [1,1,1,5,1] => 259
101000010 => [1,1,1,4,1,1] => 461
101000011 => [1,1,1,4,2] => 664
101000100 => [1,1,1,3,1,2] => 1016
101000101 => [1,1,1,3,1,1,1] => 379
101000110 => [1,1,1,3,2,1] => 1421
101000111 => [1,1,1,3,3] => 784
101001000 => [1,1,1,2,1,3] => 728
101001001 => [1,1,1,2,1,2,1] => 1099
101001010 => [1,1,1,2,1,1,1,1] => 125
101001011 => [1,1,1,2,1,1,2] => 496
101001100 => [1,1,1,2,2,2] => 1856
101001101 => [1,1,1,2,2,1,1] => 1051
101001110 => [1,1,1,2,3,1] => 1253
101001111 => [1,1,1,2,4] => 448
101010000 => [1,1,1,1,1,4] => 56
101010001 => [1,1,1,1,1,3,1] => 133
101010010 => [1,1,1,1,1,2,1,1] => 83
101010011 => [1,1,1,1,1,2,2] => 160
101010100 => [1,1,1,1,1,1,1,2] => 8
101010101 => [1,1,1,1,1,1,1,1,1] => 1
101010110 => [1,1,1,1,1,1,2,1] => 35
101010111 => [1,1,1,1,1,1,3] => 28
101011000 => [1,1,1,1,2,3] => 350
101011001 => [1,1,1,1,2,2,1] => 595
101011010 => [1,1,1,1,2,1,1,1] => 125
101011011 => [1,1,1,1,2,1,2] => 370
101011100 => [1,1,1,1,3,2] => 470
101011101 => [1,1,1,1,3,1,1] => 295
101011110 => [1,1,1,1,4,1] => 245
101011111 => [1,1,1,1,5] => 70
101100000 => [1,1,2,5] => 350
101100001 => [1,1,2,4,1] => 1351
101100010 => [1,1,2,3,1,1] => 1889
101100011 => [1,1,2,3,2] => 2890
101100100 => [1,1,2,2,1,2] => 2990
101100101 => [1,1,2,2,1,1,1] => 1051
101100110 => [1,1,2,2,2,1] => 4529
101100111 => [1,1,2,2,3] => 2590
101101000 => [1,1,2,1,1,3] => 812
101101001 => [1,1,2,1,1,2,1] => 1141
101101010 => [1,1,2,1,1,1,1,1] => 83
101101011 => [1,1,2,1,1,1,2] => 412
101101100 => [1,1,2,1,2,2] => 2780
101101101 => [1,1,2,1,2,1,1] => 1513
101101110 => [1,1,2,1,3,1] => 2051
101101111 => [1,1,2,1,4] => 784
101110000 => [1,1,3,4] => 728
101110001 => [1,1,3,3,1] => 2107
101110010 => [1,1,3,2,1,1] => 1889
101110011 => [1,1,3,2,2] => 3268
101110100 => [1,1,3,1,1,2] => 1100
101110101 => [1,1,3,1,1,1,1] => 295
101110110 => [1,1,3,1,2,1] => 2261
101110111 => [1,1,3,1,3] => 1456
101111000 => [1,1,4,3] => 812
101111001 => [1,1,4,2,1] => 1519
101111010 => [1,1,4,1,1,1] => 461
101111011 => [1,1,4,1,2] => 1168
101111100 => [1,1,5,2] => 512
101111101 => [1,1,5,1,1] => 379
101111110 => [1,1,6,1] => 161
101111111 => [1,1,7] => 28
110000000 => [2,7] => 35
110000001 => [2,6,1] => 208
110000010 => [2,5,1,1] => 512
110000011 => [2,5,2] => 685
110000100 => [2,4,1,2] => 1667
110000101 => [2,4,1,1,1] => 664
110000110 => [2,4,2,1] => 2144
110000111 => [2,4,3] => 1141
110001000 => [2,3,1,3] => 2261
110001001 => [2,3,1,2,1] => 3526
110001010 => [2,3,1,1,1,1] => 470
110001011 => [2,3,1,1,2] => 1735
110001100 => [2,3,2,2] => 4985
110001101 => [2,3,2,1,1] => 2890
110001110 => [2,3,3,1] => 3194
110001111 => [2,3,4] => 1099
110010000 => [2,2,1,4] => 1421
110010001 => [2,2,1,3,1] => 3736
110010010 => [2,2,1,2,1,1] => 2780
110010011 => [2,2,1,2,2] => 5095
110010100 => [2,2,1,1,1,2] => 785
110010101 => [2,2,1,1,1,1,1] => 160
110010110 => [2,2,1,1,2,1] => 2144
110010111 => [2,2,1,1,3] => 1519
110011000 => [2,2,2,3] => 4529
110011001 => [2,2,2,2,1] => 7936
110011010 => [2,2,2,1,1,1] => 1856
110011011 => [2,2,2,1,2] => 5263
110011100 => [2,2,3,2] => 4985
110011101 => [2,2,3,1,1] => 3268
110011110 => [2,2,4,1] => 2312
110011111 => [2,2,5] => 595
110100000 => [2,1,1,5] => 245
110100001 => [2,1,1,4,1] => 880
110100010 => [2,1,1,3,1,1] => 1100
110100011 => [2,1,1,3,2] => 1735
110100100 => [2,1,1,2,1,2] => 1457
110100101 => [2,1,1,2,1,1,1] => 496
110100110 => [2,1,1,2,2,1] => 2312
110100111 => [2,1,1,2,3] => 1351
110101000 => [2,1,1,1,1,3] => 161
110101001 => [2,1,1,1,1,2,1] => 208
110101010 => [2,1,1,1,1,1,1,1] => 8
110101011 => [2,1,1,1,1,1,2] => 55
110101100 => [2,1,1,1,2,2] => 785
110101101 => [2,1,1,1,2,1,1] => 412
110101110 => [2,1,1,1,3,1] => 632
110101111 => [2,1,1,1,4] => 259
110110000 => [2,1,2,4] => 1253
110110001 => [2,1,2,3,1] => 3526
110110010 => [2,1,2,2,1,1] => 2990
110110011 => [2,1,2,2,2] => 5263
110110100 => [2,1,2,1,1,2] => 1457
110110101 => [2,1,2,1,1,1,1] => 370
110110110 => [2,1,2,1,2,1] => 3194
110110111 => [2,1,2,1,3] => 2107
110111000 => [2,1,3,3] => 2051
110111001 => [2,1,3,2,1] => 3736
110111010 => [2,1,3,1,1,1] => 1016
110111011 => [2,1,3,1,2] => 2701
110111100 => [2,1,4,2] => 1667
110111101 => [2,1,4,1,1] => 1168
110111110 => [2,1,5,1] => 632
110111111 => [2,1,6] => 133
111000000 => [3,6] => 83
111000001 => [3,5,1] => 412
111000010 => [3,4,1,1] => 812
111000011 => [3,4,2] => 1141
111000100 => [3,3,1,2] => 2051
111000101 => [3,3,1,1,1] => 784
111000110 => [3,3,2,1] => 2780
111000111 => [3,3,3] => 1513
111001000 => [3,2,1,3] => 1889
111001001 => [3,2,1,2,1] => 2890
111001010 => [3,2,1,1,1,1] => 350
111001011 => [3,2,1,1,2] => 1351
111001100 => [3,2,2,2] => 4529
111001101 => [3,2,2,1,1] => 2590
111001110 => [3,2,3,1] => 2990
111001111 => [3,2,4] => 1051
111010000 => [3,1,1,4] => 461
111010001 => [3,1,1,3,1] => 1168
111010010 => [3,1,1,2,1,1] => 812
111010011 => [3,1,1,2,2] => 1519
111010100 => [3,1,1,1,1,2] => 161
111010101 => [3,1,1,1,1,1,1] => 28
111010110 => [3,1,1,1,2,1] => 512
111010111 => [3,1,1,1,3] => 379
111011000 => [3,1,2,3] => 1889
111011001 => [3,1,2,2,1] => 3268
111011010 => [3,1,2,1,1,1] => 728
111011011 => [3,1,2,1,2] => 2107
111011100 => [3,1,3,2] => 2261
111011101 => [3,1,3,1,1] => 1456
111011110 => [3,1,4,1] => 1100
111011111 => [3,1,5] => 295
111100000 => [4,5] => 125
111100001 => [4,4,1] => 496
111100010 => [4,3,1,1] => 728
111100011 => [4,3,2] => 1099
111100100 => [4,2,1,2] => 1253
111100101 => [4,2,1,1,1] => 448
111100110 => [4,2,2,1] => 1856
111100111 => [4,2,3] => 1051
111101000 => [4,1,1,3] => 461
111101001 => [4,1,1,2,1] => 664
111101010 => [4,1,1,1,1,1] => 56
111101011 => [4,1,1,1,2] => 259
111101100 => [4,1,2,2] => 1421
111101101 => [4,1,2,1,1] => 784
111101110 => [4,1,3,1] => 1016
111101111 => [4,1,4] => 379
111110000 => [5,4] => 125
111110001 => [5,3,1] => 370
111110010 => [5,2,1,1] => 350
111110011 => [5,2,2] => 595
111110100 => [5,1,1,2] => 245
111110101 => [5,1,1,1,1] => 70
111110110 => [5,1,2,1] => 470
111110111 => [5,1,3] => 295
111111000 => [6,3] => 83
111111001 => [6,2,1] => 160
111111010 => [6,1,1,1] => 56
111111011 => [6,1,2] => 133
111111100 => [7,2] => 35
111111101 => [7,1,1] => 28
111111110 => [8,1] => 8
111111111 => [9] => 1
1010101010 => [1,1,1,1,1,1,1,1,1,1] => 1
1010101100 => [1,1,1,1,1,1,2,2] => 231
1010110010 => [1,1,1,1,2,2,1,1] => 2149
1010110100 => [1,1,1,1,2,1,1,2] => 999
1010111000 => [1,1,1,1,3,3] => 1674
1011001010 => [1,1,2,2,1,1,1,1] => 2149
1011001100 => [1,1,2,2,2,2] => 28839
1011010010 => [1,1,2,1,1,2,1,1] => 3961
1011010100 => [1,1,2,1,1,1,1,2] => 711
1011011000 => [1,1,2,1,2,3] => 10206
1011100010 => [1,1,3,3,1,1] => 8371
1011100100 => [1,1,3,2,1,2] => 13941
1011101000 => [1,1,3,1,1,3] => 4536
1011110000 => [1,1,4,4] => 2064
1100101010 => [2,2,1,1,1,1,1,1] => 231
1100101100 => [2,2,1,1,2,2] => 13991
1100110010 => [2,2,2,2,1,1] => 28839
1100110100 => [2,2,2,1,1,2] => 14759
1100111000 => [2,2,3,3] => 17594
1101001010 => [2,1,1,2,1,1,1,1] => 999
1101001100 => [2,1,1,2,2,2] => 14759
1101010010 => [2,1,1,1,1,2,1,1] => 711
1101010100 => [2,1,1,1,1,1,1,2] => 71
1101011000 => [2,1,1,1,2,3] => 2906
1101100010 => [2,1,2,3,1,1] => 13941
1101100100 => [2,1,2,2,1,2] => 22121
1101101000 => [2,1,2,1,1,3] => 6056
1101110000 => [2,1,3,4] => 5264
1110001010 => [3,3,1,1,1,1] => 1674
1110001100 => [3,3,2,2] => 17594
1110010010 => [3,2,1,2,1,1] => 10206
1110010100 => [3,2,1,1,1,2] => 2906
1110011000 => [3,2,2,3] => 16451
1110100010 => [3,1,1,3,1,1] => 4536
1110100100 => [3,1,1,2,1,2] => 6056
1110101000 => [3,1,1,1,1,3] => 701
1110110000 => [3,1,2,4] => 4949
1111000010 => [4,4,1,1] => 2064
1111000100 => [4,3,1,2] => 5264
1111001000 => [4,2,1,3] => 4949
1111010000 => [4,1,1,4] => 1301
1111100000 => [5,5] => 251
101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
101010101100 => [1,1,1,1,1,1,1,1,2,2] => 429
101010110010 => [1,1,1,1,1,1,2,2,1,1] => 6909
101010110100 => [1,1,1,1,1,1,2,1,1,2] => 3157
101010111000 => [1,1,1,1,1,1,3,3] => 5698
101011001010 => [1,1,1,1,2,2,1,1,1,1] => 15049
101011001100 => [1,1,1,1,2,2,2,2] => 203181
101011010010 => [1,1,1,1,2,1,1,2,1,1] => 26709
101011010100 => [1,1,1,1,2,1,1,1,1,2] => 4741
101011011000 => [1,1,1,1,2,1,2,3] => 69850
101011100010 => [1,1,1,1,3,3,1,1] => 65154
101011100100 => [1,1,1,1,3,2,1,2] => 107866
101011101000 => [1,1,1,1,3,1,1,3] => 34375
101011110000 => [1,1,1,1,4,4] => 16995
101100101010 => [1,1,2,2,1,1,1,1,1,1] => 6909
101100101100 => [1,1,2,2,1,1,2,2] => 421421
101100110010 => [1,1,2,2,2,2,1,1] => 880529
101100110100 => [1,1,2,2,2,1,1,2] => 450021
101100111000 => [1,1,2,2,3,3] => 538890
101101001010 => [1,1,2,1,1,2,1,1,1,1] => 26709
101101001100 => [1,1,2,1,1,2,2,2] => 396077
101101010010 => [1,1,2,1,1,1,1,2,1,1] => 18041
101101010100 => [1,1,2,1,1,1,1,1,1,2] => 1749
101101011000 => [1,1,2,1,1,1,2,3] => 75570
101101100010 => [1,1,2,1,2,3,1,1] => 392822
101101100100 => [1,1,2,1,2,2,1,2] => 622314
101101101000 => [1,1,2,1,2,1,1,3] => 169455
101101110000 => [1,1,2,1,3,4] => 150227
101110001010 => [1,1,3,3,1,1,1,1] => 65154
101110001100 => [1,1,3,3,2,2] => 686906
101110010010 => [1,1,3,2,1,2,1,1] => 392822
101110010100 => [1,1,3,2,1,1,1,2] => 111474
101110011000 => [1,1,3,2,2,3] => 635745
101110100010 => [1,1,3,1,1,3,1,1] => 166541
101110100100 => [1,1,3,1,1,2,1,2] => 221529
101110101000 => [1,1,3,1,1,1,1,3] => 25080
101110110000 => [1,1,3,1,2,4] => 185108
101111000010 => [1,1,4,4,1,1] => 90509
101111000100 => [1,1,4,3,1,2] => 230241
101111001000 => [1,1,4,2,1,3] => 215160
101111010000 => [1,1,4,1,1,4] => 55220
101111100000 => [1,1,5,5] => 11825
110010101010 => [2,2,1,1,1,1,1,1,1,1] => 429
110010101100 => [2,2,1,1,1,1,2,2] => 66989
110010110010 => [2,2,1,1,2,2,1,1] => 421421
110010110100 => [2,2,1,1,2,1,1,2] => 199341
110010111000 => [2,2,1,1,3,3] => 312102
110011001010 => [2,2,2,2,1,1,1,1] => 203181
110011001100 => [2,2,2,2,2,2] => 2702765
110011010010 => [2,2,2,1,1,2,1,1] => 396077
110011010100 => [2,2,2,1,1,1,1,2] => 72621
110011011000 => [2,2,2,1,2,3] => 996390
110011100010 => [2,2,3,3,1,1] => 686906
110011100100 => [2,2,3,2,1,2] => 1152546
110011101000 => [2,2,3,1,1,3] => 385395
110011110000 => [2,2,4,4] => 157475
110100101010 => [2,1,1,2,1,1,1,1,1,1] => 3157
110100101100 => [2,1,1,2,1,1,2,2] => 199341
110100110010 => [2,1,1,2,2,2,1,1] => 450021
110100110100 => [2,1,1,2,2,1,1,2] => 228205
110100111000 => [2,1,1,2,3,3] => 280774
110101001010 => [2,1,1,1,1,2,1,1,1,1] => 4741
110101001100 => [2,1,1,1,1,2,2,2] => 72621
110101010010 => [2,1,1,1,1,1,1,2,1,1] => 1749
110101010100 => [2,1,1,1,1,1,1,1,1,2] => 109
110101011000 => [2,1,1,1,1,1,2,3] => 9910
110101100010 => [2,1,1,1,2,3,1,1] => 111474
110101100100 => [2,1,1,1,2,2,1,2] => 174514
110101101000 => [2,1,1,1,2,1,1,3] => 45715
110101110000 => [2,1,1,1,3,4] => 46947
110110001010 => [2,1,2,3,1,1,1,1] => 107866
110110001100 => [2,1,2,3,2,2] => 1152546
110110010010 => [2,1,2,2,1,2,1,1] => 622314
110110010100 => [2,1,2,2,1,1,1,2] => 174514
110110011000 => [2,1,2,2,2,3] => 1022845
110110100010 => [2,1,2,1,1,3,1,1] => 221529
110110100100 => [2,1,2,1,1,2,1,2] => 291169
110110101000 => [2,1,2,1,1,1,1,3] => 30700
110110110000 => [2,1,2,1,2,4] => 262932
110111000010 => [2,1,3,4,1,1] => 230241
110111000100 => [2,1,3,3,1,2] => 578665
110111001000 => [2,1,3,2,1,3] => 527284
110111010000 => [2,1,3,1,1,4] => 123540
110111100000 => [2,1,4,5] => 39225
111000101010 => [3,3,1,1,1,1,1,1] => 5698
111000101100 => [3,3,1,1,2,2] => 312102
111000110010 => [3,3,2,2,1,1] => 538890
111000110100 => [3,3,2,1,1,2] => 280774
111000111000 => [3,3,3,3] => 315523
111001001010 => [3,2,1,2,1,1,1,1] => 69850
111001001100 => [3,2,1,2,2,2] => 996390
111001010010 => [3,2,1,1,1,2,1,1] => 75570
111001010100 => [3,2,1,1,1,1,1,2] => 9910
111001011000 => [3,2,1,1,2,3] => 251371
111001100010 => [3,2,2,3,1,1] => 635745
111001100100 => [3,2,2,2,1,2] => 1022845
111001101000 => [3,2,2,1,1,3] => 294106
111001110000 => [3,2,3,4] => 215346
111010001010 => [3,1,1,3,1,1,1,1] => 34375
111010001100 => [3,1,1,3,2,2] => 385395
111010010010 => [3,1,1,2,1,2,1,1] => 169455
111010010100 => [3,1,1,2,1,1,1,2] => 45715
111010011000 => [3,1,1,2,2,3] => 294106
111010100010 => [3,1,1,1,1,3,1,1] => 25080
111010100100 => [3,1,1,1,1,2,1,2] => 30700
111010101000 => [3,1,1,1,1,1,1,3] => 1891
111010110000 => [3,1,1,1,2,4] => 43251
111011000010 => [3,1,2,4,1,1] => 215160
111011000100 => [3,1,2,3,1,2] => 527284
111011001000 => [3,1,2,2,1,3] => 458083
111011010000 => [3,1,2,1,1,4] => 90771
111011100000 => [3,1,3,5] => 54966
111100001010 => [4,4,1,1,1,1] => 16995
111100001100 => [4,4,2,2] => 157475
111100010010 => [4,3,1,2,1,1] => 150227
111100010100 => [4,3,1,1,1,2] => 46947
111100011000 => [4,3,2,3] => 215346
111100100010 => [4,2,1,3,1,1] => 185108
111100100100 => [4,2,1,2,1,2] => 262932
111100101000 => [4,2,1,1,1,3] => 43251
111100110000 => [4,2,2,4] => 147443
111101000010 => [4,1,1,4,1,1] => 55220
111101000100 => [4,1,1,3,1,2] => 123540
111101001000 => [4,1,1,2,1,3] => 90771
111101010000 => [4,1,1,1,1,4] => 8051
111101100000 => [4,1,2,5] => 36926
111110000010 => [5,5,1,1] => 11825
111110000100 => [5,4,1,2] => 39225
111110001000 => [5,3,1,3] => 54966
111110010000 => [5,2,1,4] => 36926
111110100000 => [5,1,1,5] => 8051
111111000000 => [6,6] => 923
1111111110 => [9,1] => 9
1111111101 => [8,1,1] => 36
1101111110 => [2,1,6,1] => 1134
1011111110 => [1,1,7,1] => 244
1010111110 => [1,1,1,1,5,1] => 574
1001111110 => [1,2,6,1] => 1369
1001011110 => [1,2,1,1,4,1] => 5191
1000111110 => [1,3,5,1] => 3079
1000101110 => [1,3,1,1,3,1] => 8371
1000011110 => [1,4,4,1] => 3961
1000010110 => [1,4,1,1,2,1] => 5191
1000001110 => [1,5,3,1] => 3079
1000001010 => [1,5,1,1,1,1] => 574
1000000110 => [1,6,2,1] => 1369
1000000100 => [1,6,1,2] => 1134
1000000010 => [1,7,1,1] => 244
1000000001 => [1,8,1] => 71
1000000000 => [1,9] => 9
10000000000 => [1,10] => 10
10000000010 => [1,8,1,1] => 351
10000000110 => [1,7,2,1] => 2221
10000001110 => [1,6,3,1] => 5851
10000011110 => [1,5,4,1] => 9151
10000111110 => [1,4,5,1] => 9151
10001111110 => [1,3,6,1] => 5851
10011111110 => [1,2,7,1] => 2221
10111111110 => [1,1,8,1] => 351
11111111110 => [10,1] => 10
0111111111 => [1,9] => 9
0111111101 => [1,7,1,1] => 244
0111111001 => [1,6,2,1] => 1369
0111110001 => [1,5,3,1] => 3079
0111100001 => [1,4,4,1] => 3961
0100000001 => [1,1,7,1] => 244
0000000001 => [9,1] => 9
01111111111 => [1,10] => 10
01111111101 => [1,8,1,1] => 351
0111111011 => [1,6,1,2] => 1134
0111110101 => [1,5,1,1,1,1] => 574
0111101001 => [1,4,1,1,2,1] => 5191
0111010001 => [1,3,1,1,3,1] => 8371
0110100001 => [1,2,1,1,4,1] => 5191
0101000001 => [1,1,1,1,5,1] => 574
01000000001 => [1,1,8,1] => 351
00000000001 => [10,1] => 10
0101010101 => [1,1,1,1,1,1,1,1,1,1] => 1
0101001011 => [1,1,1,1,2,1,1,2] => 999
0101000111 => [1,1,1,1,3,3] => 1674
0100110011 => [1,1,2,2,2,2] => 28839
0100100111 => [1,1,2,1,2,3] => 10206
0100011011 => [1,1,3,2,1,2] => 13941
0100010111 => [1,1,3,1,1,3] => 4536
0100001111 => [1,1,4,4] => 2064
0011010011 => [2,2,1,1,2,2] => 13991
0011000111 => [2,2,3,3] => 17594
0010101011 => [2,1,1,1,1,1,1,2] => 71
0010010111 => [2,1,2,1,1,3] => 6056
0010001111 => [2,1,3,4] => 5264
0001110011 => [3,3,2,2] => 17594
0001101011 => [3,2,1,1,1,2] => 2906
0001100111 => [3,2,2,3] => 16451
0001011101 => [3,1,1,3,1,1] => 4536
0001010111 => [3,1,1,1,1,3] => 701
0001001111 => [3,1,2,4] => 4949
0000111101 => [4,4,1,1] => 2064
0000110111 => [4,2,1,3] => 4949
0000101111 => [4,1,1,4] => 1301
0000011111 => [5,5] => 251
010101010101 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
010101001011 => [1,1,1,1,1,1,2,1,1,2] => 3157
010100101011 => [1,1,1,1,2,1,1,1,1,2] => 4741
010100100111 => [1,1,1,1,2,1,2,3] => 69850
010100011011 => [1,1,1,1,3,2,1,2] => 107866
010100010111 => [1,1,1,1,3,1,1,3] => 34375
010100001111 => [1,1,1,1,4,4] => 16995
010011010101 => [1,1,2,2,1,1,1,1,1,1] => 6909
010011010011 => [1,1,2,2,1,1,2,2] => 421421
010011001011 => [1,1,2,2,2,1,1,2] => 450021
010011000111 => [1,1,2,2,3,3] => 538890
010010110101 => [1,1,2,1,1,2,1,1,1,1] => 26709
010010110011 => [1,1,2,1,1,2,2,2] => 396077
010010101011 => [1,1,2,1,1,1,1,1,1,2] => 1749
010010011011 => [1,1,2,1,2,2,1,2] => 622314
010010010111 => [1,1,2,1,2,1,1,3] => 169455
010010001111 => [1,1,2,1,3,4] => 150227
010001110101 => [1,1,3,3,1,1,1,1] => 65154
010001101011 => [1,1,3,2,1,1,1,2] => 111474
010001011101 => [1,1,3,1,1,3,1,1] => 166541
010001011011 => [1,1,3,1,1,2,1,2] => 221529
010001010111 => [1,1,3,1,1,1,1,3] => 25080
010000111011 => [1,1,4,3,1,2] => 230241
010000110111 => [1,1,4,2,1,3] => 215160
010000101111 => [1,1,4,1,1,4] => 55220
010000011111 => [1,1,5,5] => 11825
001101010101 => [2,2,1,1,1,1,1,1,1,1] => 429
001101001011 => [2,2,1,1,2,1,1,2] => 199341
001100110011 => [2,2,2,2,2,2] => 2702765
001100100111 => [2,2,2,1,2,3] => 996390
001100011011 => [2,2,3,2,1,2] => 1152546
001100010111 => [2,2,3,1,1,3] => 385395
001100001111 => [2,2,4,4] => 157475
001011010101 => [2,1,1,2,1,1,1,1,1,1] => 3157
001011001101 => [2,1,1,2,2,2,1,1] => 450021
001011000111 => [2,1,1,2,3,3] => 280774
001010101011 => [2,1,1,1,1,1,1,1,1,2] => 109
001010010111 => [2,1,1,1,2,1,1,3] => 45715
001010001111 => [2,1,1,1,3,4] => 46947
001001110101 => [2,1,2,3,1,1,1,1] => 107866
001001011101 => [2,1,2,1,1,3,1,1] => 221529
001001010111 => [2,1,2,1,1,1,1,3] => 30700
001000110111 => [2,1,3,2,1,3] => 527284
001000101111 => [2,1,3,1,1,4] => 123540
001000011111 => [2,1,4,5] => 39225
000111010101 => [3,3,1,1,1,1,1,1] => 5698
000111010011 => [3,3,1,1,2,2] => 312102
000111001011 => [3,3,2,1,1,2] => 280774
000111000111 => [3,3,3,3] => 315523
000110110101 => [3,2,1,2,1,1,1,1] => 69850
000110110011 => [3,2,1,2,2,2] => 996390
000110101011 => [3,2,1,1,1,1,1,2] => 9910
000110011011 => [3,2,2,2,1,2] => 1022845
000110010111 => [3,2,2,1,1,3] => 294106
000110001111 => [3,2,3,4] => 215346
000101110101 => [3,1,1,3,1,1,1,1] => 34375
000101101011 => [3,1,1,2,1,1,1,2] => 45715
000101011101 => [3,1,1,1,1,3,1,1] => 25080
000101011011 => [3,1,1,1,1,2,1,2] => 30700
000101010111 => [3,1,1,1,1,1,1,3] => 1891
000100111011 => [3,1,2,3,1,2] => 527284
000100110111 => [3,1,2,2,1,3] => 458083
000100101111 => [3,1,2,1,1,4] => 90771
000100011111 => [3,1,3,5] => 54966
000011110101 => [4,4,1,1,1,1] => 16995
000011110011 => [4,4,2,2] => 157475
000011011101 => [4,2,1,3,1,1] => 185108
000011011011 => [4,2,1,2,1,2] => 262932
000011010111 => [4,2,1,1,1,3] => 43251
000011001111 => [4,2,2,4] => 147443
000010110111 => [4,1,1,2,1,3] => 90771
000010101111 => [4,1,1,1,1,4] => 8051
000010011111 => [4,1,2,5] => 36926
000001111101 => [5,5,1,1] => 11825
000001111011 => [5,4,1,2] => 39225
000001110111 => [5,3,1,3] => 54966
000001101111 => [5,2,1,4] => 36926
000001011111 => [5,1,1,5] => 8051
000000111111 => [6,6] => 923
0111111110 => [1,8,1] => 71
0000000010 => [8,1,1] => 36
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,4 4,0,8,0,4 4,0,0,8,0,4,0,0,8,0,4,0,0,0,0,4 4,0,0,0,8,0,0,0,0,8,0,0,0,8,0,0,0,0,8,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4
$F_{1} = 2\ q$
$F_{2} = 4\ q$
$F_{3} = 4\ q + 4\ q^{2}$
$F_{4} = 4\ q + 8\ q^{3} + 4\ q^{5}$
$F_{5} = 4\ q + 8\ q^{4} + 4\ q^{6} + 8\ q^{9} + 4\ q^{11} + 4\ q^{16}$
$F_{6} = 4\ q + 8\ q^{5} + 8\ q^{10} + 8\ q^{14} + 8\ q^{19} + 8\ q^{26} + 8\ q^{35} + 8\ q^{40} + 4\ q^{61}$
$F_{7} = 4\ q + 8\ q^{6} + 8\ q^{15} + 12\ q^{20} + 4\ q^{29} + 8\ q^{34} + 8\ q^{50} + 8\ q^{55} + 8\ q^{64} + 4\ q^{71} + 8\ q^{78} + 4\ q^{90} + 8\ q^{99} + 8\ q^{111} + 4\ q^{132} + 8\ q^{155} + 4\ q^{169} + 8\ q^{181} + 4\ q^{272}$
$F_{8} = 4\ q + 8\ q^{7} + 8\ q^{21} + 8\ q^{27} + 8\ q^{35} + 4\ q^{41} + 8\ q^{55} + 4\ q^{69} + 8\ q^{85} + 8\ q^{99} + 8\ q^{105} + 8\ q^{125} + 8\ q^{133} + 8\ q^{155} + 4\ q^{181} + 8\ q^{189} + 8\ q^{203} + 8\ q^{217} + 8\ q^{245} + 8\ q^{259} + 16\ q^{315} + 8\ q^{323} + 4\ q^{365} + 8\ q^{407} + 8\ q^{413} + 4\ q^{449} + 8\ q^{477} + 8\ q^{531} + 8\ q^{573} + 4\ q^{589} + 8\ q^{643} + 8\ q^{791} + 8\ q^{875} + 8\ q^{917} + 4\ q^{1385}$
$F_{9} = 4\ q + 8\ q^{8} + 8\ q^{28} + 8\ q^{35} + 4\ q^{55} + 8\ q^{56} + 4\ q^{70} + 8\ q^{83} + 8\ q^{125} + 8\ q^{133} + 8\ q^{160} + 8\ q^{161} + 8\ q^{208} + 8\ q^{245} + 8\ q^{259} + 8\ q^{295} + 8\ q^{350} + 8\ q^{370} + 8\ q^{379} + 8\ q^{412} + 4\ q^{448} + 8\ q^{461} + 8\ q^{470} + 8\ q^{496} + 8\ q^{512} + 8\ q^{595} + 8\ q^{632} + 8\ q^{664} + 4\ q^{685} + 8\ q^{728} + 8\ q^{784} + 8\ q^{785} + 8\ q^{812} + 4\ q^{880} + 8\ q^{1016} + 8\ q^{1051} + 8\ q^{1099} + 8\ q^{1100} + 8\ q^{1141} + 8\ q^{1168} + 8\ q^{1253} + 8\ q^{1351} + 8\ q^{1421} + 4\ q^{1456} + 8\ q^{1457} + 4\ q^{1513} + 8\ q^{1519} + 8\ q^{1667} + 8\ q^{1735} + 8\ q^{1856} + 8\ q^{1889} + 8\ q^{2051} + 8\ q^{2107} + 8\ q^{2144} + 8\ q^{2261} + 8\ q^{2312} + 4\ q^{2590} + 4\ q^{2701} + 8\ q^{2780} + 8\ q^{2890} + 8\ q^{2990} + 8\ q^{3194} + 8\ q^{3268} + 8\ q^{3526} + 8\ q^{3736} + 8\ q^{4529} + 8\ q^{4985} + 4\ q^{5095} + 8\ q^{5263} + 4\ q^{7936}$
Description
The number of ribbon shaped standard tableaux.
A ribbon is a connected skew shape which does not contain a $2\times 2$ square. The set of ribbon shapes are therefore in bijection with integer compositons, the parts of the composition specify the row lengths. This statistic records the number of standard tableaux of the given shape.
This is also the size of the preimage of the map 'descent composition' Mp00071descent composition from permutations to integer compositions: reading a tableau from bottom to top we obtain a permutation whose descent set is as prescribed.
For a composition $c=c_1,\dots,c_k$ of $n$, the number of ribbon shaped standard tableaux equals
$$ \sum_d (-1)^{k-\ell} \binom{n}{d_1, d_2, \dots, d_\ell}, $$
where the sum is over all coarsenings of $c$ obtained by replacing consecutive summands by their sum, see [sec 14.4, 1]
A ribbon is a connected skew shape which does not contain a $2\times 2$ square. The set of ribbon shapes are therefore in bijection with integer compositons, the parts of the composition specify the row lengths. This statistic records the number of standard tableaux of the given shape.
This is also the size of the preimage of the map 'descent composition' Mp00071descent composition from permutations to integer compositions: reading a tableau from bottom to top we obtain a permutation whose descent set is as prescribed.
For a composition $c=c_1,\dots,c_k$ of $n$, the number of ribbon shaped standard tableaux equals
$$ \sum_d (-1)^{k-\ell} \binom{n}{d_1, d_2, \dots, d_\ell}, $$
where the sum is over all coarsenings of $c$ obtained by replacing consecutive summands by their sum, see [sec 14.4, 1]
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
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