Identifier
-
Mp00178:
Binary words
—to composition⟶
Integer compositions
St001486: Integer compositions ⟶ ℤ
Values
0 => [2] => 2
1 => [1,1] => 2
00 => [3] => 2
01 => [2,1] => 3
10 => [1,2] => 3
11 => [1,1,1] => 2
000 => [4] => 2
001 => [3,1] => 3
010 => [2,2] => 4
011 => [2,1,1] => 3
100 => [1,3] => 3
101 => [1,2,1] => 4
110 => [1,1,2] => 3
111 => [1,1,1,1] => 2
0000 => [5] => 2
0001 => [4,1] => 3
0010 => [3,2] => 4
0011 => [3,1,1] => 3
0100 => [2,3] => 4
0101 => [2,2,1] => 5
0110 => [2,1,2] => 4
0111 => [2,1,1,1] => 3
1000 => [1,4] => 3
1001 => [1,3,1] => 4
1010 => [1,2,2] => 5
1011 => [1,2,1,1] => 4
1100 => [1,1,3] => 3
1101 => [1,1,2,1] => 4
1110 => [1,1,1,2] => 3
1111 => [1,1,1,1,1] => 2
00000 => [6] => 2
00001 => [5,1] => 3
00010 => [4,2] => 4
00011 => [4,1,1] => 3
00100 => [3,3] => 4
00101 => [3,2,1] => 5
00110 => [3,1,2] => 4
00111 => [3,1,1,1] => 3
01000 => [2,4] => 4
01001 => [2,3,1] => 5
01010 => [2,2,2] => 6
01011 => [2,2,1,1] => 5
01100 => [2,1,3] => 4
01101 => [2,1,2,1] => 5
01110 => [2,1,1,2] => 4
01111 => [2,1,1,1,1] => 3
10000 => [1,5] => 3
10001 => [1,4,1] => 4
10010 => [1,3,2] => 5
10011 => [1,3,1,1] => 4
10100 => [1,2,3] => 5
10101 => [1,2,2,1] => 6
10110 => [1,2,1,2] => 5
10111 => [1,2,1,1,1] => 4
11000 => [1,1,4] => 3
11001 => [1,1,3,1] => 4
11010 => [1,1,2,2] => 5
11011 => [1,1,2,1,1] => 4
11100 => [1,1,1,3] => 3
11101 => [1,1,1,2,1] => 4
11110 => [1,1,1,1,2] => 3
11111 => [1,1,1,1,1,1] => 2
000000 => [7] => 2
000001 => [6,1] => 3
000010 => [5,2] => 4
000011 => [5,1,1] => 3
000100 => [4,3] => 4
000101 => [4,2,1] => 5
000110 => [4,1,2] => 4
000111 => [4,1,1,1] => 3
001000 => [3,4] => 4
001001 => [3,3,1] => 5
001010 => [3,2,2] => 6
001011 => [3,2,1,1] => 5
001100 => [3,1,3] => 4
001101 => [3,1,2,1] => 5
001110 => [3,1,1,2] => 4
001111 => [3,1,1,1,1] => 3
010000 => [2,5] => 4
010001 => [2,4,1] => 5
010010 => [2,3,2] => 6
010011 => [2,3,1,1] => 5
010100 => [2,2,3] => 6
010101 => [2,2,2,1] => 7
010110 => [2,2,1,2] => 6
010111 => [2,2,1,1,1] => 5
011000 => [2,1,4] => 4
011001 => [2,1,3,1] => 5
011010 => [2,1,2,2] => 6
011011 => [2,1,2,1,1] => 5
011100 => [2,1,1,3] => 4
011101 => [2,1,1,2,1] => 5
011110 => [2,1,1,1,2] => 4
011111 => [2,1,1,1,1,1] => 3
100000 => [1,6] => 3
100001 => [1,5,1] => 4
100010 => [1,4,2] => 5
100011 => [1,4,1,1] => 4
100100 => [1,3,3] => 5
100101 => [1,3,2,1] => 6
100110 => [1,3,1,2] => 5
>>> Load all 1023 entries. <<<100111 => [1,3,1,1,1] => 4
101000 => [1,2,4] => 5
101001 => [1,2,3,1] => 6
101010 => [1,2,2,2] => 7
101011 => [1,2,2,1,1] => 6
101100 => [1,2,1,3] => 5
101101 => [1,2,1,2,1] => 6
101110 => [1,2,1,1,2] => 5
101111 => [1,2,1,1,1,1] => 4
110000 => [1,1,5] => 3
110001 => [1,1,4,1] => 4
110010 => [1,1,3,2] => 5
110011 => [1,1,3,1,1] => 4
110100 => [1,1,2,3] => 5
110101 => [1,1,2,2,1] => 6
110110 => [1,1,2,1,2] => 5
110111 => [1,1,2,1,1,1] => 4
111000 => [1,1,1,4] => 3
111001 => [1,1,1,3,1] => 4
111010 => [1,1,1,2,2] => 5
111011 => [1,1,1,2,1,1] => 4
111100 => [1,1,1,1,3] => 3
111101 => [1,1,1,1,2,1] => 4
111110 => [1,1,1,1,1,2] => 3
111111 => [1,1,1,1,1,1,1] => 2
0000000 => [8] => 2
0000001 => [7,1] => 3
0000010 => [6,2] => 4
0000011 => [6,1,1] => 3
0000100 => [5,3] => 4
0000101 => [5,2,1] => 5
0000110 => [5,1,2] => 4
0000111 => [5,1,1,1] => 3
0001000 => [4,4] => 4
0001001 => [4,3,1] => 5
0001010 => [4,2,2] => 6
0001011 => [4,2,1,1] => 5
0001100 => [4,1,3] => 4
0001101 => [4,1,2,1] => 5
0001110 => [4,1,1,2] => 4
0001111 => [4,1,1,1,1] => 3
0010000 => [3,5] => 4
0010001 => [3,4,1] => 5
0010010 => [3,3,2] => 6
0010011 => [3,3,1,1] => 5
0010100 => [3,2,3] => 6
0010101 => [3,2,2,1] => 7
0010110 => [3,2,1,2] => 6
0010111 => [3,2,1,1,1] => 5
0011000 => [3,1,4] => 4
0011001 => [3,1,3,1] => 5
0011010 => [3,1,2,2] => 6
0011011 => [3,1,2,1,1] => 5
0011100 => [3,1,1,3] => 4
0011101 => [3,1,1,2,1] => 5
0011110 => [3,1,1,1,2] => 4
0011111 => [3,1,1,1,1,1] => 3
0100000 => [2,6] => 4
0100001 => [2,5,1] => 5
0100010 => [2,4,2] => 6
0100011 => [2,4,1,1] => 5
0100100 => [2,3,3] => 6
0100101 => [2,3,2,1] => 7
0100110 => [2,3,1,2] => 6
0100111 => [2,3,1,1,1] => 5
0101000 => [2,2,4] => 6
0101001 => [2,2,3,1] => 7
0101010 => [2,2,2,2] => 8
0101011 => [2,2,2,1,1] => 7
0101100 => [2,2,1,3] => 6
0101101 => [2,2,1,2,1] => 7
0101110 => [2,2,1,1,2] => 6
0101111 => [2,2,1,1,1,1] => 5
0110000 => [2,1,5] => 4
0110001 => [2,1,4,1] => 5
0110010 => [2,1,3,2] => 6
0110011 => [2,1,3,1,1] => 5
0110100 => [2,1,2,3] => 6
0110101 => [2,1,2,2,1] => 7
0110110 => [2,1,2,1,2] => 6
0110111 => [2,1,2,1,1,1] => 5
0111000 => [2,1,1,4] => 4
0111001 => [2,1,1,3,1] => 5
0111010 => [2,1,1,2,2] => 6
0111011 => [2,1,1,2,1,1] => 5
0111100 => [2,1,1,1,3] => 4
0111101 => [2,1,1,1,2,1] => 5
0111110 => [2,1,1,1,1,2] => 4
0111111 => [2,1,1,1,1,1,1] => 3
1000000 => [1,7] => 3
1000001 => [1,6,1] => 4
1000010 => [1,5,2] => 5
1000011 => [1,5,1,1] => 4
1000100 => [1,4,3] => 5
1000101 => [1,4,2,1] => 6
1000110 => [1,4,1,2] => 5
1000111 => [1,4,1,1,1] => 4
1001000 => [1,3,4] => 5
1001001 => [1,3,3,1] => 6
1001010 => [1,3,2,2] => 7
1001011 => [1,3,2,1,1] => 6
1001100 => [1,3,1,3] => 5
1001101 => [1,3,1,2,1] => 6
1001110 => [1,3,1,1,2] => 5
1001111 => [1,3,1,1,1,1] => 4
1010000 => [1,2,5] => 5
1010001 => [1,2,4,1] => 6
1010010 => [1,2,3,2] => 7
1010011 => [1,2,3,1,1] => 6
1010100 => [1,2,2,3] => 7
1010101 => [1,2,2,2,1] => 8
1010110 => [1,2,2,1,2] => 7
1010111 => [1,2,2,1,1,1] => 6
1011000 => [1,2,1,4] => 5
1011001 => [1,2,1,3,1] => 6
1011010 => [1,2,1,2,2] => 7
1011011 => [1,2,1,2,1,1] => 6
1011100 => [1,2,1,1,3] => 5
1011101 => [1,2,1,1,2,1] => 6
1011110 => [1,2,1,1,1,2] => 5
1011111 => [1,2,1,1,1,1,1] => 4
1100000 => [1,1,6] => 3
1100001 => [1,1,5,1] => 4
1100010 => [1,1,4,2] => 5
1100011 => [1,1,4,1,1] => 4
1100100 => [1,1,3,3] => 5
1100101 => [1,1,3,2,1] => 6
1100110 => [1,1,3,1,2] => 5
1100111 => [1,1,3,1,1,1] => 4
1101000 => [1,1,2,4] => 5
1101001 => [1,1,2,3,1] => 6
1101010 => [1,1,2,2,2] => 7
1101011 => [1,1,2,2,1,1] => 6
1101100 => [1,1,2,1,3] => 5
1101101 => [1,1,2,1,2,1] => 6
1101110 => [1,1,2,1,1,2] => 5
1101111 => [1,1,2,1,1,1,1] => 4
1110000 => [1,1,1,5] => 3
1110001 => [1,1,1,4,1] => 4
1110010 => [1,1,1,3,2] => 5
1110011 => [1,1,1,3,1,1] => 4
1110100 => [1,1,1,2,3] => 5
1110101 => [1,1,1,2,2,1] => 6
1110110 => [1,1,1,2,1,2] => 5
1110111 => [1,1,1,2,1,1,1] => 4
1111000 => [1,1,1,1,4] => 3
1111001 => [1,1,1,1,3,1] => 4
1111010 => [1,1,1,1,2,2] => 5
1111011 => [1,1,1,1,2,1,1] => 4
1111100 => [1,1,1,1,1,3] => 3
1111101 => [1,1,1,1,1,2,1] => 4
1111110 => [1,1,1,1,1,1,2] => 3
1111111 => [1,1,1,1,1,1,1,1] => 2
00000000 => [9] => 2
00000001 => [8,1] => 3
00000010 => [7,2] => 4
00000011 => [7,1,1] => 3
00000100 => [6,3] => 4
00000101 => [6,2,1] => 5
00000110 => [6,1,2] => 4
00000111 => [6,1,1,1] => 3
00001000 => [5,4] => 4
00001001 => [5,3,1] => 5
00001010 => [5,2,2] => 6
00001011 => [5,2,1,1] => 5
00001100 => [5,1,3] => 4
00001101 => [5,1,2,1] => 5
00001110 => [5,1,1,2] => 4
00001111 => [5,1,1,1,1] => 3
00010000 => [4,5] => 4
00010001 => [4,4,1] => 5
00010010 => [4,3,2] => 6
00010011 => [4,3,1,1] => 5
00010100 => [4,2,3] => 6
00010101 => [4,2,2,1] => 7
00010110 => [4,2,1,2] => 6
00010111 => [4,2,1,1,1] => 5
00011000 => [4,1,4] => 4
00011001 => [4,1,3,1] => 5
00011010 => [4,1,2,2] => 6
00011011 => [4,1,2,1,1] => 5
00011100 => [4,1,1,3] => 4
00011101 => [4,1,1,2,1] => 5
00011110 => [4,1,1,1,2] => 4
00011111 => [4,1,1,1,1,1] => 3
00100000 => [3,6] => 4
00100001 => [3,5,1] => 5
00100010 => [3,4,2] => 6
00100011 => [3,4,1,1] => 5
00100100 => [3,3,3] => 6
00100101 => [3,3,2,1] => 7
00100110 => [3,3,1,2] => 6
00100111 => [3,3,1,1,1] => 5
00101000 => [3,2,4] => 6
00101001 => [3,2,3,1] => 7
00101010 => [3,2,2,2] => 8
00101011 => [3,2,2,1,1] => 7
00101100 => [3,2,1,3] => 6
00101101 => [3,2,1,2,1] => 7
00101110 => [3,2,1,1,2] => 6
00101111 => [3,2,1,1,1,1] => 5
00110000 => [3,1,5] => 4
00110001 => [3,1,4,1] => 5
00110010 => [3,1,3,2] => 6
00110011 => [3,1,3,1,1] => 5
00110100 => [3,1,2,3] => 6
00110101 => [3,1,2,2,1] => 7
00110110 => [3,1,2,1,2] => 6
00110111 => [3,1,2,1,1,1] => 5
00111000 => [3,1,1,4] => 4
00111001 => [3,1,1,3,1] => 5
00111010 => [3,1,1,2,2] => 6
00111011 => [3,1,1,2,1,1] => 5
00111100 => [3,1,1,1,3] => 4
00111101 => [3,1,1,1,2,1] => 5
00111110 => [3,1,1,1,1,2] => 4
00111111 => [3,1,1,1,1,1,1] => 3
01000000 => [2,7] => 4
01000001 => [2,6,1] => 5
01000010 => [2,5,2] => 6
01000011 => [2,5,1,1] => 5
01000100 => [2,4,3] => 6
01000101 => [2,4,2,1] => 7
01000110 => [2,4,1,2] => 6
01000111 => [2,4,1,1,1] => 5
01001000 => [2,3,4] => 6
01001001 => [2,3,3,1] => 7
01001010 => [2,3,2,2] => 8
01001011 => [2,3,2,1,1] => 7
01001100 => [2,3,1,3] => 6
01001101 => [2,3,1,2,1] => 7
01001110 => [2,3,1,1,2] => 6
01001111 => [2,3,1,1,1,1] => 5
01010000 => [2,2,5] => 6
01010001 => [2,2,4,1] => 7
01010010 => [2,2,3,2] => 8
01010011 => [2,2,3,1,1] => 7
01010100 => [2,2,2,3] => 8
01010101 => [2,2,2,2,1] => 9
01010110 => [2,2,2,1,2] => 8
01010111 => [2,2,2,1,1,1] => 7
01011000 => [2,2,1,4] => 6
01011001 => [2,2,1,3,1] => 7
01011010 => [2,2,1,2,2] => 8
01011011 => [2,2,1,2,1,1] => 7
01011100 => [2,2,1,1,3] => 6
01011101 => [2,2,1,1,2,1] => 7
01011110 => [2,2,1,1,1,2] => 6
01011111 => [2,2,1,1,1,1,1] => 5
01100000 => [2,1,6] => 4
01100001 => [2,1,5,1] => 5
01100010 => [2,1,4,2] => 6
01100011 => [2,1,4,1,1] => 5
01100100 => [2,1,3,3] => 6
01100101 => [2,1,3,2,1] => 7
01100110 => [2,1,3,1,2] => 6
01100111 => [2,1,3,1,1,1] => 5
01101000 => [2,1,2,4] => 6
01101001 => [2,1,2,3,1] => 7
01101010 => [2,1,2,2,2] => 8
01101011 => [2,1,2,2,1,1] => 7
01101100 => [2,1,2,1,3] => 6
01101101 => [2,1,2,1,2,1] => 7
01101110 => [2,1,2,1,1,2] => 6
01101111 => [2,1,2,1,1,1,1] => 5
01110000 => [2,1,1,5] => 4
01110001 => [2,1,1,4,1] => 5
01110010 => [2,1,1,3,2] => 6
01110011 => [2,1,1,3,1,1] => 5
01110100 => [2,1,1,2,3] => 6
01110101 => [2,1,1,2,2,1] => 7
01110110 => [2,1,1,2,1,2] => 6
01110111 => [2,1,1,2,1,1,1] => 5
01111000 => [2,1,1,1,4] => 4
01111001 => [2,1,1,1,3,1] => 5
01111010 => [2,1,1,1,2,2] => 6
01111011 => [2,1,1,1,2,1,1] => 5
01111100 => [2,1,1,1,1,3] => 4
01111101 => [2,1,1,1,1,2,1] => 5
01111110 => [2,1,1,1,1,1,2] => 4
01111111 => [2,1,1,1,1,1,1,1] => 3
10000000 => [1,8] => 3
10000001 => [1,7,1] => 4
10000010 => [1,6,2] => 5
10000011 => [1,6,1,1] => 4
10000100 => [1,5,3] => 5
10000101 => [1,5,2,1] => 6
10000110 => [1,5,1,2] => 5
10000111 => [1,5,1,1,1] => 4
10001000 => [1,4,4] => 5
10001001 => [1,4,3,1] => 6
10001010 => [1,4,2,2] => 7
10001011 => [1,4,2,1,1] => 6
10001100 => [1,4,1,3] => 5
10001101 => [1,4,1,2,1] => 6
10001110 => [1,4,1,1,2] => 5
10001111 => [1,4,1,1,1,1] => 4
10010000 => [1,3,5] => 5
10010001 => [1,3,4,1] => 6
10010010 => [1,3,3,2] => 7
10010011 => [1,3,3,1,1] => 6
10010100 => [1,3,2,3] => 7
10010101 => [1,3,2,2,1] => 8
10010110 => [1,3,2,1,2] => 7
10010111 => [1,3,2,1,1,1] => 6
10011000 => [1,3,1,4] => 5
10011001 => [1,3,1,3,1] => 6
10011010 => [1,3,1,2,2] => 7
10011011 => [1,3,1,2,1,1] => 6
10011100 => [1,3,1,1,3] => 5
10011101 => [1,3,1,1,2,1] => 6
10011110 => [1,3,1,1,1,2] => 5
10011111 => [1,3,1,1,1,1,1] => 4
10100000 => [1,2,6] => 5
10100001 => [1,2,5,1] => 6
10100010 => [1,2,4,2] => 7
10100011 => [1,2,4,1,1] => 6
10100100 => [1,2,3,3] => 7
10100101 => [1,2,3,2,1] => 8
10100110 => [1,2,3,1,2] => 7
10100111 => [1,2,3,1,1,1] => 6
10101000 => [1,2,2,4] => 7
10101001 => [1,2,2,3,1] => 8
10101010 => [1,2,2,2,2] => 9
10101011 => [1,2,2,2,1,1] => 8
10101100 => [1,2,2,1,3] => 7
10101101 => [1,2,2,1,2,1] => 8
10101110 => [1,2,2,1,1,2] => 7
10101111 => [1,2,2,1,1,1,1] => 6
10110000 => [1,2,1,5] => 5
10110001 => [1,2,1,4,1] => 6
10110010 => [1,2,1,3,2] => 7
10110011 => [1,2,1,3,1,1] => 6
10110100 => [1,2,1,2,3] => 7
10110101 => [1,2,1,2,2,1] => 8
10110110 => [1,2,1,2,1,2] => 7
10110111 => [1,2,1,2,1,1,1] => 6
10111000 => [1,2,1,1,4] => 5
10111001 => [1,2,1,1,3,1] => 6
10111010 => [1,2,1,1,2,2] => 7
10111011 => [1,2,1,1,2,1,1] => 6
10111100 => [1,2,1,1,1,3] => 5
10111101 => [1,2,1,1,1,2,1] => 6
10111110 => [1,2,1,1,1,1,2] => 5
10111111 => [1,2,1,1,1,1,1,1] => 4
11000000 => [1,1,7] => 3
11000001 => [1,1,6,1] => 4
11000010 => [1,1,5,2] => 5
11000011 => [1,1,5,1,1] => 4
11000100 => [1,1,4,3] => 5
11000101 => [1,1,4,2,1] => 6
11000110 => [1,1,4,1,2] => 5
11000111 => [1,1,4,1,1,1] => 4
11001000 => [1,1,3,4] => 5
11001001 => [1,1,3,3,1] => 6
11001010 => [1,1,3,2,2] => 7
11001011 => [1,1,3,2,1,1] => 6
11001100 => [1,1,3,1,3] => 5
11001101 => [1,1,3,1,2,1] => 6
11001110 => [1,1,3,1,1,2] => 5
11001111 => [1,1,3,1,1,1,1] => 4
11010000 => [1,1,2,5] => 5
11010001 => [1,1,2,4,1] => 6
11010010 => [1,1,2,3,2] => 7
11010011 => [1,1,2,3,1,1] => 6
11010100 => [1,1,2,2,3] => 7
11010101 => [1,1,2,2,2,1] => 8
11010110 => [1,1,2,2,1,2] => 7
11010111 => [1,1,2,2,1,1,1] => 6
11011000 => [1,1,2,1,4] => 5
11011001 => [1,1,2,1,3,1] => 6
11011010 => [1,1,2,1,2,2] => 7
11011011 => [1,1,2,1,2,1,1] => 6
11011100 => [1,1,2,1,1,3] => 5
11011101 => [1,1,2,1,1,2,1] => 6
11011110 => [1,1,2,1,1,1,2] => 5
11011111 => [1,1,2,1,1,1,1,1] => 4
11100000 => [1,1,1,6] => 3
11100001 => [1,1,1,5,1] => 4
11100010 => [1,1,1,4,2] => 5
11100011 => [1,1,1,4,1,1] => 4
11100100 => [1,1,1,3,3] => 5
11100101 => [1,1,1,3,2,1] => 6
11100110 => [1,1,1,3,1,2] => 5
11100111 => [1,1,1,3,1,1,1] => 4
11101000 => [1,1,1,2,4] => 5
11101001 => [1,1,1,2,3,1] => 6
11101010 => [1,1,1,2,2,2] => 7
11101011 => [1,1,1,2,2,1,1] => 6
11101100 => [1,1,1,2,1,3] => 5
11101101 => [1,1,1,2,1,2,1] => 6
11101110 => [1,1,1,2,1,1,2] => 5
11101111 => [1,1,1,2,1,1,1,1] => 4
11110000 => [1,1,1,1,5] => 3
11110001 => [1,1,1,1,4,1] => 4
11110010 => [1,1,1,1,3,2] => 5
11110011 => [1,1,1,1,3,1,1] => 4
11110100 => [1,1,1,1,2,3] => 5
11110101 => [1,1,1,1,2,2,1] => 6
11110110 => [1,1,1,1,2,1,2] => 5
11110111 => [1,1,1,1,2,1,1,1] => 4
11111000 => [1,1,1,1,1,4] => 3
11111001 => [1,1,1,1,1,3,1] => 4
11111010 => [1,1,1,1,1,2,2] => 5
11111011 => [1,1,1,1,1,2,1,1] => 4
11111100 => [1,1,1,1,1,1,3] => 3
11111101 => [1,1,1,1,1,1,2,1] => 4
11111110 => [1,1,1,1,1,1,1,2] => 3
11111111 => [1,1,1,1,1,1,1,1,1] => 2
000000000 => [10] => 2
000000001 => [9,1] => 3
000000010 => [8,2] => 4
000000011 => [8,1,1] => 3
000000100 => [7,3] => 4
000000101 => [7,2,1] => 5
000000110 => [7,1,2] => 4
000000111 => [7,1,1,1] => 3
000001000 => [6,4] => 4
000001001 => [6,3,1] => 5
000001010 => [6,2,2] => 6
000001011 => [6,2,1,1] => 5
000001100 => [6,1,3] => 4
000001101 => [6,1,2,1] => 5
000001110 => [6,1,1,2] => 4
000001111 => [6,1,1,1,1] => 3
000010000 => [5,5] => 4
000010001 => [5,4,1] => 5
000010010 => [5,3,2] => 6
000010011 => [5,3,1,1] => 5
000010100 => [5,2,3] => 6
000010101 => [5,2,2,1] => 7
000010110 => [5,2,1,2] => 6
000010111 => [5,2,1,1,1] => 5
000011000 => [5,1,4] => 4
000011001 => [5,1,3,1] => 5
000011010 => [5,1,2,2] => 6
000011011 => [5,1,2,1,1] => 5
000011100 => [5,1,1,3] => 4
000011101 => [5,1,1,2,1] => 5
000011110 => [5,1,1,1,2] => 4
000011111 => [5,1,1,1,1,1] => 3
000100000 => [4,6] => 4
000100001 => [4,5,1] => 5
000100010 => [4,4,2] => 6
000100011 => [4,4,1,1] => 5
000100100 => [4,3,3] => 6
000100101 => [4,3,2,1] => 7
000100110 => [4,3,1,2] => 6
000100111 => [4,3,1,1,1] => 5
000101000 => [4,2,4] => 6
000101001 => [4,2,3,1] => 7
000101010 => [4,2,2,2] => 8
000101011 => [4,2,2,1,1] => 7
000101100 => [4,2,1,3] => 6
000101101 => [4,2,1,2,1] => 7
000101110 => [4,2,1,1,2] => 6
000101111 => [4,2,1,1,1,1] => 5
000110000 => [4,1,5] => 4
000110001 => [4,1,4,1] => 5
000110010 => [4,1,3,2] => 6
000110011 => [4,1,3,1,1] => 5
000110100 => [4,1,2,3] => 6
000110101 => [4,1,2,2,1] => 7
000110110 => [4,1,2,1,2] => 6
000110111 => [4,1,2,1,1,1] => 5
000111000 => [4,1,1,4] => 4
000111001 => [4,1,1,3,1] => 5
000111010 => [4,1,1,2,2] => 6
000111011 => [4,1,1,2,1,1] => 5
000111100 => [4,1,1,1,3] => 4
000111101 => [4,1,1,1,2,1] => 5
000111110 => [4,1,1,1,1,2] => 4
000111111 => [4,1,1,1,1,1,1] => 3
001000000 => [3,7] => 4
001000001 => [3,6,1] => 5
001000010 => [3,5,2] => 6
001000011 => [3,5,1,1] => 5
001000100 => [3,4,3] => 6
001000101 => [3,4,2,1] => 7
001000110 => [3,4,1,2] => 6
001000111 => [3,4,1,1,1] => 5
001001000 => [3,3,4] => 6
001001001 => [3,3,3,1] => 7
001001010 => [3,3,2,2] => 8
001001011 => [3,3,2,1,1] => 7
001001100 => [3,3,1,3] => 6
001001101 => [3,3,1,2,1] => 7
001001110 => [3,3,1,1,2] => 6
001001111 => [3,3,1,1,1,1] => 5
001010000 => [3,2,5] => 6
001010001 => [3,2,4,1] => 7
001010010 => [3,2,3,2] => 8
001010011 => [3,2,3,1,1] => 7
001010100 => [3,2,2,3] => 8
001010101 => [3,2,2,2,1] => 9
001010110 => [3,2,2,1,2] => 8
001010111 => [3,2,2,1,1,1] => 7
001011000 => [3,2,1,4] => 6
001011001 => [3,2,1,3,1] => 7
001011010 => [3,2,1,2,2] => 8
001011011 => [3,2,1,2,1,1] => 7
001011100 => [3,2,1,1,3] => 6
001011101 => [3,2,1,1,2,1] => 7
001011110 => [3,2,1,1,1,2] => 6
001011111 => [3,2,1,1,1,1,1] => 5
001100000 => [3,1,6] => 4
001100001 => [3,1,5,1] => 5
001100010 => [3,1,4,2] => 6
001100011 => [3,1,4,1,1] => 5
001100100 => [3,1,3,3] => 6
001100101 => [3,1,3,2,1] => 7
001100110 => [3,1,3,1,2] => 6
001100111 => [3,1,3,1,1,1] => 5
001101000 => [3,1,2,4] => 6
001101001 => [3,1,2,3,1] => 7
001101010 => [3,1,2,2,2] => 8
001101011 => [3,1,2,2,1,1] => 7
001101100 => [3,1,2,1,3] => 6
001101101 => [3,1,2,1,2,1] => 7
001101110 => [3,1,2,1,1,2] => 6
001101111 => [3,1,2,1,1,1,1] => 5
001110000 => [3,1,1,5] => 4
001110001 => [3,1,1,4,1] => 5
001110010 => [3,1,1,3,2] => 6
001110011 => [3,1,1,3,1,1] => 5
001110100 => [3,1,1,2,3] => 6
001110101 => [3,1,1,2,2,1] => 7
001110110 => [3,1,1,2,1,2] => 6
001110111 => [3,1,1,2,1,1,1] => 5
001111000 => [3,1,1,1,4] => 4
001111001 => [3,1,1,1,3,1] => 5
001111010 => [3,1,1,1,2,2] => 6
001111011 => [3,1,1,1,2,1,1] => 5
001111100 => [3,1,1,1,1,3] => 4
001111101 => [3,1,1,1,1,2,1] => 5
001111110 => [3,1,1,1,1,1,2] => 4
001111111 => [3,1,1,1,1,1,1,1] => 3
010000000 => [2,8] => 4
010000001 => [2,7,1] => 5
010000010 => [2,6,2] => 6
010000011 => [2,6,1,1] => 5
010000100 => [2,5,3] => 6
010000101 => [2,5,2,1] => 7
010000110 => [2,5,1,2] => 6
010000111 => [2,5,1,1,1] => 5
010001000 => [2,4,4] => 6
010001001 => [2,4,3,1] => 7
010001010 => [2,4,2,2] => 8
010001011 => [2,4,2,1,1] => 7
010001100 => [2,4,1,3] => 6
010001101 => [2,4,1,2,1] => 7
010001110 => [2,4,1,1,2] => 6
010001111 => [2,4,1,1,1,1] => 5
010010000 => [2,3,5] => 6
010010001 => [2,3,4,1] => 7
010010010 => [2,3,3,2] => 8
010010011 => [2,3,3,1,1] => 7
010010100 => [2,3,2,3] => 8
010010101 => [2,3,2,2,1] => 9
010010110 => [2,3,2,1,2] => 8
010010111 => [2,3,2,1,1,1] => 7
010011000 => [2,3,1,4] => 6
010011001 => [2,3,1,3,1] => 7
010011010 => [2,3,1,2,2] => 8
010011011 => [2,3,1,2,1,1] => 7
010011100 => [2,3,1,1,3] => 6
010011101 => [2,3,1,1,2,1] => 7
010011110 => [2,3,1,1,1,2] => 6
010011111 => [2,3,1,1,1,1,1] => 5
010100000 => [2,2,6] => 6
010100001 => [2,2,5,1] => 7
010100010 => [2,2,4,2] => 8
010100011 => [2,2,4,1,1] => 7
010100100 => [2,2,3,3] => 8
010100101 => [2,2,3,2,1] => 9
010100110 => [2,2,3,1,2] => 8
010100111 => [2,2,3,1,1,1] => 7
010101000 => [2,2,2,4] => 8
010101001 => [2,2,2,3,1] => 9
010101010 => [2,2,2,2,2] => 10
010101011 => [2,2,2,2,1,1] => 9
010101100 => [2,2,2,1,3] => 8
010101101 => [2,2,2,1,2,1] => 9
010101110 => [2,2,2,1,1,2] => 8
010101111 => [2,2,2,1,1,1,1] => 7
010110000 => [2,2,1,5] => 6
010110001 => [2,2,1,4,1] => 7
010110010 => [2,2,1,3,2] => 8
010110011 => [2,2,1,3,1,1] => 7
010110100 => [2,2,1,2,3] => 8
010110101 => [2,2,1,2,2,1] => 9
010110110 => [2,2,1,2,1,2] => 8
010110111 => [2,2,1,2,1,1,1] => 7
010111000 => [2,2,1,1,4] => 6
010111001 => [2,2,1,1,3,1] => 7
010111010 => [2,2,1,1,2,2] => 8
010111011 => [2,2,1,1,2,1,1] => 7
010111100 => [2,2,1,1,1,3] => 6
010111101 => [2,2,1,1,1,2,1] => 7
010111110 => [2,2,1,1,1,1,2] => 6
010111111 => [2,2,1,1,1,1,1,1] => 5
011000000 => [2,1,7] => 4
011000001 => [2,1,6,1] => 5
011000010 => [2,1,5,2] => 6
011000011 => [2,1,5,1,1] => 5
011000100 => [2,1,4,3] => 6
011000101 => [2,1,4,2,1] => 7
011000110 => [2,1,4,1,2] => 6
011000111 => [2,1,4,1,1,1] => 5
011001000 => [2,1,3,4] => 6
011001001 => [2,1,3,3,1] => 7
011001010 => [2,1,3,2,2] => 8
011001011 => [2,1,3,2,1,1] => 7
011001100 => [2,1,3,1,3] => 6
011001101 => [2,1,3,1,2,1] => 7
011001110 => [2,1,3,1,1,2] => 6
011001111 => [2,1,3,1,1,1,1] => 5
011010000 => [2,1,2,5] => 6
011010001 => [2,1,2,4,1] => 7
011010010 => [2,1,2,3,2] => 8
011010011 => [2,1,2,3,1,1] => 7
011010100 => [2,1,2,2,3] => 8
011010101 => [2,1,2,2,2,1] => 9
011010110 => [2,1,2,2,1,2] => 8
011010111 => [2,1,2,2,1,1,1] => 7
011011000 => [2,1,2,1,4] => 6
011011001 => [2,1,2,1,3,1] => 7
011011010 => [2,1,2,1,2,2] => 8
011011011 => [2,1,2,1,2,1,1] => 7
011011100 => [2,1,2,1,1,3] => 6
011011101 => [2,1,2,1,1,2,1] => 7
011011110 => [2,1,2,1,1,1,2] => 6
011011111 => [2,1,2,1,1,1,1,1] => 5
011100000 => [2,1,1,6] => 4
011100001 => [2,1,1,5,1] => 5
011100010 => [2,1,1,4,2] => 6
011100011 => [2,1,1,4,1,1] => 5
011100100 => [2,1,1,3,3] => 6
011100101 => [2,1,1,3,2,1] => 7
011100110 => [2,1,1,3,1,2] => 6
011100111 => [2,1,1,3,1,1,1] => 5
011101000 => [2,1,1,2,4] => 6
011101001 => [2,1,1,2,3,1] => 7
011101010 => [2,1,1,2,2,2] => 8
011101011 => [2,1,1,2,2,1,1] => 7
011101100 => [2,1,1,2,1,3] => 6
011101101 => [2,1,1,2,1,2,1] => 7
011101110 => [2,1,1,2,1,1,2] => 6
011101111 => [2,1,1,2,1,1,1,1] => 5
011110000 => [2,1,1,1,5] => 4
011110001 => [2,1,1,1,4,1] => 5
011110010 => [2,1,1,1,3,2] => 6
011110011 => [2,1,1,1,3,1,1] => 5
011110100 => [2,1,1,1,2,3] => 6
011110101 => [2,1,1,1,2,2,1] => 7
011110110 => [2,1,1,1,2,1,2] => 6
011110111 => [2,1,1,1,2,1,1,1] => 5
011111000 => [2,1,1,1,1,4] => 4
011111001 => [2,1,1,1,1,3,1] => 5
011111010 => [2,1,1,1,1,2,2] => 6
011111011 => [2,1,1,1,1,2,1,1] => 5
011111100 => [2,1,1,1,1,1,3] => 4
011111101 => [2,1,1,1,1,1,2,1] => 5
011111110 => [2,1,1,1,1,1,1,2] => 4
011111111 => [2,1,1,1,1,1,1,1,1] => 3
100000000 => [1,9] => 3
100000001 => [1,8,1] => 4
100000010 => [1,7,2] => 5
100000011 => [1,7,1,1] => 4
100000100 => [1,6,3] => 5
100000101 => [1,6,2,1] => 6
100000110 => [1,6,1,2] => 5
100000111 => [1,6,1,1,1] => 4
100001000 => [1,5,4] => 5
100001001 => [1,5,3,1] => 6
100001010 => [1,5,2,2] => 7
100001011 => [1,5,2,1,1] => 6
100001100 => [1,5,1,3] => 5
100001101 => [1,5,1,2,1] => 6
100001110 => [1,5,1,1,2] => 5
100001111 => [1,5,1,1,1,1] => 4
100010000 => [1,4,5] => 5
100010001 => [1,4,4,1] => 6
100010010 => [1,4,3,2] => 7
100010011 => [1,4,3,1,1] => 6
100010100 => [1,4,2,3] => 7
100010101 => [1,4,2,2,1] => 8
100010110 => [1,4,2,1,2] => 7
100010111 => [1,4,2,1,1,1] => 6
100011000 => [1,4,1,4] => 5
100011001 => [1,4,1,3,1] => 6
100011010 => [1,4,1,2,2] => 7
100011011 => [1,4,1,2,1,1] => 6
100011100 => [1,4,1,1,3] => 5
100011101 => [1,4,1,1,2,1] => 6
100011110 => [1,4,1,1,1,2] => 5
100011111 => [1,4,1,1,1,1,1] => 4
100100000 => [1,3,6] => 5
100100001 => [1,3,5,1] => 6
100100010 => [1,3,4,2] => 7
100100011 => [1,3,4,1,1] => 6
100100100 => [1,3,3,3] => 7
100100101 => [1,3,3,2,1] => 8
100100110 => [1,3,3,1,2] => 7
100100111 => [1,3,3,1,1,1] => 6
100101000 => [1,3,2,4] => 7
100101001 => [1,3,2,3,1] => 8
100101010 => [1,3,2,2,2] => 9
100101011 => [1,3,2,2,1,1] => 8
100101100 => [1,3,2,1,3] => 7
100101101 => [1,3,2,1,2,1] => 8
100101110 => [1,3,2,1,1,2] => 7
100101111 => [1,3,2,1,1,1,1] => 6
100110000 => [1,3,1,5] => 5
100110001 => [1,3,1,4,1] => 6
100110010 => [1,3,1,3,2] => 7
100110011 => [1,3,1,3,1,1] => 6
100110100 => [1,3,1,2,3] => 7
100110101 => [1,3,1,2,2,1] => 8
100110110 => [1,3,1,2,1,2] => 7
100110111 => [1,3,1,2,1,1,1] => 6
100111000 => [1,3,1,1,4] => 5
100111001 => [1,3,1,1,3,1] => 6
100111010 => [1,3,1,1,2,2] => 7
100111011 => [1,3,1,1,2,1,1] => 6
100111100 => [1,3,1,1,1,3] => 5
100111101 => [1,3,1,1,1,2,1] => 6
100111110 => [1,3,1,1,1,1,2] => 5
100111111 => [1,3,1,1,1,1,1,1] => 4
101000000 => [1,2,7] => 5
101000001 => [1,2,6,1] => 6
101000010 => [1,2,5,2] => 7
101000011 => [1,2,5,1,1] => 6
101000100 => [1,2,4,3] => 7
101000101 => [1,2,4,2,1] => 8
101000110 => [1,2,4,1,2] => 7
101000111 => [1,2,4,1,1,1] => 6
101001000 => [1,2,3,4] => 7
101001001 => [1,2,3,3,1] => 8
101001010 => [1,2,3,2,2] => 9
101001011 => [1,2,3,2,1,1] => 8
101001100 => [1,2,3,1,3] => 7
101001101 => [1,2,3,1,2,1] => 8
101001110 => [1,2,3,1,1,2] => 7
101001111 => [1,2,3,1,1,1,1] => 6
101010000 => [1,2,2,5] => 7
101010001 => [1,2,2,4,1] => 8
101010010 => [1,2,2,3,2] => 9
101010011 => [1,2,2,3,1,1] => 8
101010100 => [1,2,2,2,3] => 9
101010101 => [1,2,2,2,2,1] => 10
101010110 => [1,2,2,2,1,2] => 9
101010111 => [1,2,2,2,1,1,1] => 8
101011000 => [1,2,2,1,4] => 7
101011001 => [1,2,2,1,3,1] => 8
101011010 => [1,2,2,1,2,2] => 9
101011011 => [1,2,2,1,2,1,1] => 8
101011100 => [1,2,2,1,1,3] => 7
101011101 => [1,2,2,1,1,2,1] => 8
101011110 => [1,2,2,1,1,1,2] => 7
101011111 => [1,2,2,1,1,1,1,1] => 6
101100000 => [1,2,1,6] => 5
101100001 => [1,2,1,5,1] => 6
101100010 => [1,2,1,4,2] => 7
101100011 => [1,2,1,4,1,1] => 6
101100100 => [1,2,1,3,3] => 7
101100101 => [1,2,1,3,2,1] => 8
101100110 => [1,2,1,3,1,2] => 7
101100111 => [1,2,1,3,1,1,1] => 6
101101000 => [1,2,1,2,4] => 7
101101001 => [1,2,1,2,3,1] => 8
101101010 => [1,2,1,2,2,2] => 9
101101011 => [1,2,1,2,2,1,1] => 8
101101100 => [1,2,1,2,1,3] => 7
101101101 => [1,2,1,2,1,2,1] => 8
101101110 => [1,2,1,2,1,1,2] => 7
101101111 => [1,2,1,2,1,1,1,1] => 6
101110000 => [1,2,1,1,5] => 5
101110001 => [1,2,1,1,4,1] => 6
101110010 => [1,2,1,1,3,2] => 7
101110011 => [1,2,1,1,3,1,1] => 6
101110100 => [1,2,1,1,2,3] => 7
101110101 => [1,2,1,1,2,2,1] => 8
101110110 => [1,2,1,1,2,1,2] => 7
101110111 => [1,2,1,1,2,1,1,1] => 6
101111000 => [1,2,1,1,1,4] => 5
101111001 => [1,2,1,1,1,3,1] => 6
101111010 => [1,2,1,1,1,2,2] => 7
101111011 => [1,2,1,1,1,2,1,1] => 6
101111100 => [1,2,1,1,1,1,3] => 5
101111101 => [1,2,1,1,1,1,2,1] => 6
101111110 => [1,2,1,1,1,1,1,2] => 5
101111111 => [1,2,1,1,1,1,1,1,1] => 4
110000000 => [1,1,8] => 3
110000001 => [1,1,7,1] => 4
110000010 => [1,1,6,2] => 5
110000011 => [1,1,6,1,1] => 4
110000100 => [1,1,5,3] => 5
110000101 => [1,1,5,2,1] => 6
110000110 => [1,1,5,1,2] => 5
110000111 => [1,1,5,1,1,1] => 4
110001000 => [1,1,4,4] => 5
110001001 => [1,1,4,3,1] => 6
110001010 => [1,1,4,2,2] => 7
110001011 => [1,1,4,2,1,1] => 6
110001100 => [1,1,4,1,3] => 5
110001101 => [1,1,4,1,2,1] => 6
110001110 => [1,1,4,1,1,2] => 5
110001111 => [1,1,4,1,1,1,1] => 4
110010000 => [1,1,3,5] => 5
110010001 => [1,1,3,4,1] => 6
110010010 => [1,1,3,3,2] => 7
110010011 => [1,1,3,3,1,1] => 6
110010100 => [1,1,3,2,3] => 7
110010101 => [1,1,3,2,2,1] => 8
110010110 => [1,1,3,2,1,2] => 7
110010111 => [1,1,3,2,1,1,1] => 6
110011000 => [1,1,3,1,4] => 5
110011001 => [1,1,3,1,3,1] => 6
110011010 => [1,1,3,1,2,2] => 7
110011011 => [1,1,3,1,2,1,1] => 6
110011100 => [1,1,3,1,1,3] => 5
110011101 => [1,1,3,1,1,2,1] => 6
110011110 => [1,1,3,1,1,1,2] => 5
110011111 => [1,1,3,1,1,1,1,1] => 4
110100000 => [1,1,2,6] => 5
110100001 => [1,1,2,5,1] => 6
110100010 => [1,1,2,4,2] => 7
110100011 => [1,1,2,4,1,1] => 6
110100100 => [1,1,2,3,3] => 7
110100101 => [1,1,2,3,2,1] => 8
110100110 => [1,1,2,3,1,2] => 7
110100111 => [1,1,2,3,1,1,1] => 6
110101000 => [1,1,2,2,4] => 7
110101001 => [1,1,2,2,3,1] => 8
110101010 => [1,1,2,2,2,2] => 9
110101011 => [1,1,2,2,2,1,1] => 8
110101100 => [1,1,2,2,1,3] => 7
110101101 => [1,1,2,2,1,2,1] => 8
110101110 => [1,1,2,2,1,1,2] => 7
110101111 => [1,1,2,2,1,1,1,1] => 6
110110000 => [1,1,2,1,5] => 5
110110001 => [1,1,2,1,4,1] => 6
110110010 => [1,1,2,1,3,2] => 7
110110011 => [1,1,2,1,3,1,1] => 6
110110100 => [1,1,2,1,2,3] => 7
110110101 => [1,1,2,1,2,2,1] => 8
110110110 => [1,1,2,1,2,1,2] => 7
110110111 => [1,1,2,1,2,1,1,1] => 6
110111000 => [1,1,2,1,1,4] => 5
110111001 => [1,1,2,1,1,3,1] => 6
110111010 => [1,1,2,1,1,2,2] => 7
110111011 => [1,1,2,1,1,2,1,1] => 6
110111100 => [1,1,2,1,1,1,3] => 5
110111101 => [1,1,2,1,1,1,2,1] => 6
110111110 => [1,1,2,1,1,1,1,2] => 5
110111111 => [1,1,2,1,1,1,1,1,1] => 4
111000000 => [1,1,1,7] => 3
111000001 => [1,1,1,6,1] => 4
111000010 => [1,1,1,5,2] => 5
111000011 => [1,1,1,5,1,1] => 4
111000100 => [1,1,1,4,3] => 5
111000101 => [1,1,1,4,2,1] => 6
111000110 => [1,1,1,4,1,2] => 5
111000111 => [1,1,1,4,1,1,1] => 4
111001000 => [1,1,1,3,4] => 5
111001001 => [1,1,1,3,3,1] => 6
111001010 => [1,1,1,3,2,2] => 7
111001011 => [1,1,1,3,2,1,1] => 6
111001100 => [1,1,1,3,1,3] => 5
111001101 => [1,1,1,3,1,2,1] => 6
111001110 => [1,1,1,3,1,1,2] => 5
111001111 => [1,1,1,3,1,1,1,1] => 4
111010000 => [1,1,1,2,5] => 5
111010001 => [1,1,1,2,4,1] => 6
111010010 => [1,1,1,2,3,2] => 7
111010011 => [1,1,1,2,3,1,1] => 6
111010100 => [1,1,1,2,2,3] => 7
111010101 => [1,1,1,2,2,2,1] => 8
111010110 => [1,1,1,2,2,1,2] => 7
111010111 => [1,1,1,2,2,1,1,1] => 6
111011000 => [1,1,1,2,1,4] => 5
111011001 => [1,1,1,2,1,3,1] => 6
111011010 => [1,1,1,2,1,2,2] => 7
111011011 => [1,1,1,2,1,2,1,1] => 6
111011100 => [1,1,1,2,1,1,3] => 5
111011101 => [1,1,1,2,1,1,2,1] => 6
111011110 => [1,1,1,2,1,1,1,2] => 5
111011111 => [1,1,1,2,1,1,1,1,1] => 4
111100000 => [1,1,1,1,6] => 3
111100001 => [1,1,1,1,5,1] => 4
111100010 => [1,1,1,1,4,2] => 5
111100011 => [1,1,1,1,4,1,1] => 4
111100100 => [1,1,1,1,3,3] => 5
111100101 => [1,1,1,1,3,2,1] => 6
111100110 => [1,1,1,1,3,1,2] => 5
111100111 => [1,1,1,1,3,1,1,1] => 4
111101000 => [1,1,1,1,2,4] => 5
111101001 => [1,1,1,1,2,3,1] => 6
111101010 => [1,1,1,1,2,2,2] => 7
111101011 => [1,1,1,1,2,2,1,1] => 6
111101100 => [1,1,1,1,2,1,3] => 5
111101101 => [1,1,1,1,2,1,2,1] => 6
111101110 => [1,1,1,1,2,1,1,2] => 5
111101111 => [1,1,1,1,2,1,1,1,1] => 4
111110000 => [1,1,1,1,1,5] => 3
111110001 => [1,1,1,1,1,4,1] => 4
111110010 => [1,1,1,1,1,3,2] => 5
111110011 => [1,1,1,1,1,3,1,1] => 4
111110100 => [1,1,1,1,1,2,3] => 5
111110101 => [1,1,1,1,1,2,2,1] => 6
111110110 => [1,1,1,1,1,2,1,2] => 5
111110111 => [1,1,1,1,1,2,1,1,1] => 4
111111000 => [1,1,1,1,1,1,4] => 3
111111001 => [1,1,1,1,1,1,3,1] => 4
111111010 => [1,1,1,1,1,1,2,2] => 5
111111011 => [1,1,1,1,1,1,2,1,1] => 4
111111100 => [1,1,1,1,1,1,1,3] => 3
111111101 => [1,1,1,1,1,1,1,2,1] => 4
111111110 => [1,1,1,1,1,1,1,1,2] => 3
111111111 => [1,1,1,1,1,1,1,1,1,1] => 2
=> [1] => 1
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Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 2,4,2 2,6,6,2 2,8,12,8,2 2,10,20,20,10,2 2,12,30,40,30,12,2 2,14,42,70,70,42,14,2 2,16,56,112,140,112,56,16,2
$F_{1} = 2\ q^{2}$
$F_{2} = 2\ q^{2} + 2\ q^{3}$
$F_{3} = 2\ q^{2} + 4\ q^{3} + 2\ q^{4}$
$F_{4} = 2\ q^{2} + 6\ q^{3} + 6\ q^{4} + 2\ q^{5}$
$F_{5} = 2\ q^{2} + 8\ q^{3} + 12\ q^{4} + 8\ q^{5} + 2\ q^{6}$
$F_{6} = 2\ q^{2} + 10\ q^{3} + 20\ q^{4} + 20\ q^{5} + 10\ q^{6} + 2\ q^{7}$
$F_{7} = 2\ q^{2} + 12\ q^{3} + 30\ q^{4} + 40\ q^{5} + 30\ q^{6} + 12\ q^{7} + 2\ q^{8}$
$F_{8} = 2\ q^{2} + 14\ q^{3} + 42\ q^{4} + 70\ q^{5} + 70\ q^{6} + 42\ q^{7} + 14\ q^{8} + 2\ q^{9}$
$F_{9} = 2\ q^{2} + 16\ q^{3} + 56\ q^{4} + 112\ q^{5} + 140\ q^{6} + 112\ q^{7} + 56\ q^{8} + 16\ q^{9} + 2\ q^{10}$
Description
The number of corners of the ribbon associated with an integer composition.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
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