Identifier
-
Mp00178:
Binary words
—to composition⟶
Integer compositions
St000382: Integer compositions ⟶ ℤ
Values
0 => [2] => 2
1 => [1,1] => 1
00 => [3] => 3
01 => [2,1] => 2
10 => [1,2] => 1
11 => [1,1,1] => 1
000 => [4] => 4
001 => [3,1] => 3
010 => [2,2] => 2
011 => [2,1,1] => 2
100 => [1,3] => 1
101 => [1,2,1] => 1
110 => [1,1,2] => 1
111 => [1,1,1,1] => 1
0000 => [5] => 5
0001 => [4,1] => 4
0010 => [3,2] => 3
0011 => [3,1,1] => 3
0100 => [2,3] => 2
0101 => [2,2,1] => 2
0110 => [2,1,2] => 2
0111 => [2,1,1,1] => 2
1000 => [1,4] => 1
1001 => [1,3,1] => 1
1010 => [1,2,2] => 1
1011 => [1,2,1,1] => 1
1100 => [1,1,3] => 1
1101 => [1,1,2,1] => 1
1110 => [1,1,1,2] => 1
1111 => [1,1,1,1,1] => 1
00000 => [6] => 6
00001 => [5,1] => 5
00010 => [4,2] => 4
00011 => [4,1,1] => 4
00100 => [3,3] => 3
00101 => [3,2,1] => 3
00110 => [3,1,2] => 3
00111 => [3,1,1,1] => 3
01000 => [2,4] => 2
01001 => [2,3,1] => 2
01010 => [2,2,2] => 2
01011 => [2,2,1,1] => 2
01100 => [2,1,3] => 2
01101 => [2,1,2,1] => 2
01110 => [2,1,1,2] => 2
01111 => [2,1,1,1,1] => 2
10000 => [1,5] => 1
10001 => [1,4,1] => 1
10010 => [1,3,2] => 1
10011 => [1,3,1,1] => 1
10100 => [1,2,3] => 1
10101 => [1,2,2,1] => 1
10110 => [1,2,1,2] => 1
10111 => [1,2,1,1,1] => 1
11000 => [1,1,4] => 1
11001 => [1,1,3,1] => 1
11010 => [1,1,2,2] => 1
11011 => [1,1,2,1,1] => 1
11100 => [1,1,1,3] => 1
11101 => [1,1,1,2,1] => 1
11110 => [1,1,1,1,2] => 1
11111 => [1,1,1,1,1,1] => 1
000000 => [7] => 7
000001 => [6,1] => 6
000010 => [5,2] => 5
000011 => [5,1,1] => 5
000100 => [4,3] => 4
000101 => [4,2,1] => 4
000110 => [4,1,2] => 4
000111 => [4,1,1,1] => 4
001000 => [3,4] => 3
001001 => [3,3,1] => 3
001010 => [3,2,2] => 3
001011 => [3,2,1,1] => 3
001100 => [3,1,3] => 3
001101 => [3,1,2,1] => 3
001110 => [3,1,1,2] => 3
001111 => [3,1,1,1,1] => 3
010000 => [2,5] => 2
010001 => [2,4,1] => 2
010010 => [2,3,2] => 2
010011 => [2,3,1,1] => 2
010100 => [2,2,3] => 2
010101 => [2,2,2,1] => 2
010110 => [2,2,1,2] => 2
010111 => [2,2,1,1,1] => 2
011000 => [2,1,4] => 2
011001 => [2,1,3,1] => 2
011010 => [2,1,2,2] => 2
011011 => [2,1,2,1,1] => 2
011100 => [2,1,1,3] => 2
011101 => [2,1,1,2,1] => 2
011110 => [2,1,1,1,2] => 2
011111 => [2,1,1,1,1,1] => 2
100000 => [1,6] => 1
100001 => [1,5,1] => 1
100010 => [1,4,2] => 1
100011 => [1,4,1,1] => 1
100100 => [1,3,3] => 1
100101 => [1,3,2,1] => 1
100110 => [1,3,1,2] => 1
>>> Load all 1110 entries. <<<100111 => [1,3,1,1,1] => 1
101000 => [1,2,4] => 1
101001 => [1,2,3,1] => 1
101010 => [1,2,2,2] => 1
101011 => [1,2,2,1,1] => 1
101100 => [1,2,1,3] => 1
101101 => [1,2,1,2,1] => 1
101110 => [1,2,1,1,2] => 1
101111 => [1,2,1,1,1,1] => 1
110000 => [1,1,5] => 1
110001 => [1,1,4,1] => 1
110010 => [1,1,3,2] => 1
110011 => [1,1,3,1,1] => 1
110100 => [1,1,2,3] => 1
110101 => [1,1,2,2,1] => 1
110110 => [1,1,2,1,2] => 1
110111 => [1,1,2,1,1,1] => 1
111000 => [1,1,1,4] => 1
111001 => [1,1,1,3,1] => 1
111010 => [1,1,1,2,2] => 1
111011 => [1,1,1,2,1,1] => 1
111100 => [1,1,1,1,3] => 1
111101 => [1,1,1,1,2,1] => 1
111110 => [1,1,1,1,1,2] => 1
111111 => [1,1,1,1,1,1,1] => 1
0000000 => [8] => 8
0000001 => [7,1] => 7
0000010 => [6,2] => 6
0000011 => [6,1,1] => 6
0000100 => [5,3] => 5
0000101 => [5,2,1] => 5
0000110 => [5,1,2] => 5
0000111 => [5,1,1,1] => 5
0001000 => [4,4] => 4
0001001 => [4,3,1] => 4
0001010 => [4,2,2] => 4
0001011 => [4,2,1,1] => 4
0001100 => [4,1,3] => 4
0001101 => [4,1,2,1] => 4
0001110 => [4,1,1,2] => 4
0001111 => [4,1,1,1,1] => 4
0010000 => [3,5] => 3
0010001 => [3,4,1] => 3
0010010 => [3,3,2] => 3
0010011 => [3,3,1,1] => 3
0010100 => [3,2,3] => 3
0010101 => [3,2,2,1] => 3
0010110 => [3,2,1,2] => 3
0010111 => [3,2,1,1,1] => 3
0011000 => [3,1,4] => 3
0011001 => [3,1,3,1] => 3
0011010 => [3,1,2,2] => 3
0011011 => [3,1,2,1,1] => 3
0011100 => [3,1,1,3] => 3
0011101 => [3,1,1,2,1] => 3
0011110 => [3,1,1,1,2] => 3
0011111 => [3,1,1,1,1,1] => 3
0100000 => [2,6] => 2
0100001 => [2,5,1] => 2
0100010 => [2,4,2] => 2
0100011 => [2,4,1,1] => 2
0100100 => [2,3,3] => 2
0100101 => [2,3,2,1] => 2
0100110 => [2,3,1,2] => 2
0100111 => [2,3,1,1,1] => 2
0101000 => [2,2,4] => 2
0101001 => [2,2,3,1] => 2
0101010 => [2,2,2,2] => 2
0101011 => [2,2,2,1,1] => 2
0101100 => [2,2,1,3] => 2
0101101 => [2,2,1,2,1] => 2
0101110 => [2,2,1,1,2] => 2
0101111 => [2,2,1,1,1,1] => 2
0110000 => [2,1,5] => 2
0110001 => [2,1,4,1] => 2
0110010 => [2,1,3,2] => 2
0110011 => [2,1,3,1,1] => 2
0110100 => [2,1,2,3] => 2
0110101 => [2,1,2,2,1] => 2
0110110 => [2,1,2,1,2] => 2
0110111 => [2,1,2,1,1,1] => 2
0111000 => [2,1,1,4] => 2
0111001 => [2,1,1,3,1] => 2
0111010 => [2,1,1,2,2] => 2
0111011 => [2,1,1,2,1,1] => 2
0111100 => [2,1,1,1,3] => 2
0111101 => [2,1,1,1,2,1] => 2
0111110 => [2,1,1,1,1,2] => 2
0111111 => [2,1,1,1,1,1,1] => 2
1000000 => [1,7] => 1
1000001 => [1,6,1] => 1
1000010 => [1,5,2] => 1
1000011 => [1,5,1,1] => 1
1000100 => [1,4,3] => 1
1000101 => [1,4,2,1] => 1
1000110 => [1,4,1,2] => 1
1000111 => [1,4,1,1,1] => 1
1001000 => [1,3,4] => 1
1001001 => [1,3,3,1] => 1
1001010 => [1,3,2,2] => 1
1001011 => [1,3,2,1,1] => 1
1001100 => [1,3,1,3] => 1
1001101 => [1,3,1,2,1] => 1
1001110 => [1,3,1,1,2] => 1
1001111 => [1,3,1,1,1,1] => 1
1010000 => [1,2,5] => 1
1010001 => [1,2,4,1] => 1
1010010 => [1,2,3,2] => 1
1010011 => [1,2,3,1,1] => 1
1010100 => [1,2,2,3] => 1
1010101 => [1,2,2,2,1] => 1
1010110 => [1,2,2,1,2] => 1
1010111 => [1,2,2,1,1,1] => 1
1011000 => [1,2,1,4] => 1
1011001 => [1,2,1,3,1] => 1
1011010 => [1,2,1,2,2] => 1
1011011 => [1,2,1,2,1,1] => 1
1011100 => [1,2,1,1,3] => 1
1011101 => [1,2,1,1,2,1] => 1
1011110 => [1,2,1,1,1,2] => 1
1011111 => [1,2,1,1,1,1,1] => 1
1100000 => [1,1,6] => 1
1100001 => [1,1,5,1] => 1
1100010 => [1,1,4,2] => 1
1100011 => [1,1,4,1,1] => 1
1100100 => [1,1,3,3] => 1
1100101 => [1,1,3,2,1] => 1
1100110 => [1,1,3,1,2] => 1
1100111 => [1,1,3,1,1,1] => 1
1101000 => [1,1,2,4] => 1
1101001 => [1,1,2,3,1] => 1
1101010 => [1,1,2,2,2] => 1
1101011 => [1,1,2,2,1,1] => 1
1101100 => [1,1,2,1,3] => 1
1101101 => [1,1,2,1,2,1] => 1
1101110 => [1,1,2,1,1,2] => 1
1101111 => [1,1,2,1,1,1,1] => 1
1110000 => [1,1,1,5] => 1
1110001 => [1,1,1,4,1] => 1
1110010 => [1,1,1,3,2] => 1
1110011 => [1,1,1,3,1,1] => 1
1110100 => [1,1,1,2,3] => 1
1110101 => [1,1,1,2,2,1] => 1
1110110 => [1,1,1,2,1,2] => 1
1110111 => [1,1,1,2,1,1,1] => 1
1111000 => [1,1,1,1,4] => 1
1111001 => [1,1,1,1,3,1] => 1
1111010 => [1,1,1,1,2,2] => 1
1111011 => [1,1,1,1,2,1,1] => 1
1111100 => [1,1,1,1,1,3] => 1
1111101 => [1,1,1,1,1,2,1] => 1
1111110 => [1,1,1,1,1,1,2] => 1
1111111 => [1,1,1,1,1,1,1,1] => 1
00000000 => [9] => 9
00000001 => [8,1] => 8
00000010 => [7,2] => 7
00000011 => [7,1,1] => 7
00000100 => [6,3] => 6
00000101 => [6,2,1] => 6
00000110 => [6,1,2] => 6
00000111 => [6,1,1,1] => 6
00001000 => [5,4] => 5
00001001 => [5,3,1] => 5
00001010 => [5,2,2] => 5
00001011 => [5,2,1,1] => 5
00001100 => [5,1,3] => 5
00001101 => [5,1,2,1] => 5
00001110 => [5,1,1,2] => 5
00001111 => [5,1,1,1,1] => 5
00010000 => [4,5] => 4
00010001 => [4,4,1] => 4
00010010 => [4,3,2] => 4
00010011 => [4,3,1,1] => 4
00010100 => [4,2,3] => 4
00010101 => [4,2,2,1] => 4
00010110 => [4,2,1,2] => 4
00010111 => [4,2,1,1,1] => 4
00011000 => [4,1,4] => 4
00011001 => [4,1,3,1] => 4
00011010 => [4,1,2,2] => 4
00011011 => [4,1,2,1,1] => 4
00011100 => [4,1,1,3] => 4
00011101 => [4,1,1,2,1] => 4
00011110 => [4,1,1,1,2] => 4
00011111 => [4,1,1,1,1,1] => 4
00100000 => [3,6] => 3
00100001 => [3,5,1] => 3
00100010 => [3,4,2] => 3
00100011 => [3,4,1,1] => 3
00100100 => [3,3,3] => 3
00100101 => [3,3,2,1] => 3
00100110 => [3,3,1,2] => 3
00100111 => [3,3,1,1,1] => 3
00101000 => [3,2,4] => 3
00101001 => [3,2,3,1] => 3
00101010 => [3,2,2,2] => 3
00101011 => [3,2,2,1,1] => 3
00101100 => [3,2,1,3] => 3
00101101 => [3,2,1,2,1] => 3
00101110 => [3,2,1,1,2] => 3
00101111 => [3,2,1,1,1,1] => 3
00110000 => [3,1,5] => 3
00110001 => [3,1,4,1] => 3
00110010 => [3,1,3,2] => 3
00110011 => [3,1,3,1,1] => 3
00110100 => [3,1,2,3] => 3
00110101 => [3,1,2,2,1] => 3
00110110 => [3,1,2,1,2] => 3
00110111 => [3,1,2,1,1,1] => 3
00111000 => [3,1,1,4] => 3
00111001 => [3,1,1,3,1] => 3
00111010 => [3,1,1,2,2] => 3
00111011 => [3,1,1,2,1,1] => 3
00111100 => [3,1,1,1,3] => 3
00111101 => [3,1,1,1,2,1] => 3
00111110 => [3,1,1,1,1,2] => 3
00111111 => [3,1,1,1,1,1,1] => 3
01000000 => [2,7] => 2
01000001 => [2,6,1] => 2
01000010 => [2,5,2] => 2
01000011 => [2,5,1,1] => 2
01000100 => [2,4,3] => 2
01000101 => [2,4,2,1] => 2
01000110 => [2,4,1,2] => 2
01000111 => [2,4,1,1,1] => 2
01001000 => [2,3,4] => 2
01001001 => [2,3,3,1] => 2
01001010 => [2,3,2,2] => 2
01001011 => [2,3,2,1,1] => 2
01001100 => [2,3,1,3] => 2
01001101 => [2,3,1,2,1] => 2
01001110 => [2,3,1,1,2] => 2
01001111 => [2,3,1,1,1,1] => 2
01010000 => [2,2,5] => 2
01010001 => [2,2,4,1] => 2
01010010 => [2,2,3,2] => 2
01010011 => [2,2,3,1,1] => 2
01010100 => [2,2,2,3] => 2
01010101 => [2,2,2,2,1] => 2
01010110 => [2,2,2,1,2] => 2
01010111 => [2,2,2,1,1,1] => 2
01011000 => [2,2,1,4] => 2
01011001 => [2,2,1,3,1] => 2
01011010 => [2,2,1,2,2] => 2
01011011 => [2,2,1,2,1,1] => 2
01011100 => [2,2,1,1,3] => 2
01011101 => [2,2,1,1,2,1] => 2
01011110 => [2,2,1,1,1,2] => 2
01011111 => [2,2,1,1,1,1,1] => 2
01100000 => [2,1,6] => 2
01100001 => [2,1,5,1] => 2
01100010 => [2,1,4,2] => 2
01100011 => [2,1,4,1,1] => 2
01100100 => [2,1,3,3] => 2
01100101 => [2,1,3,2,1] => 2
01100110 => [2,1,3,1,2] => 2
01100111 => [2,1,3,1,1,1] => 2
01101000 => [2,1,2,4] => 2
01101001 => [2,1,2,3,1] => 2
01101010 => [2,1,2,2,2] => 2
01101011 => [2,1,2,2,1,1] => 2
01101100 => [2,1,2,1,3] => 2
01101101 => [2,1,2,1,2,1] => 2
01101110 => [2,1,2,1,1,2] => 2
01101111 => [2,1,2,1,1,1,1] => 2
01110000 => [2,1,1,5] => 2
01110001 => [2,1,1,4,1] => 2
01110010 => [2,1,1,3,2] => 2
01110011 => [2,1,1,3,1,1] => 2
01110100 => [2,1,1,2,3] => 2
01110101 => [2,1,1,2,2,1] => 2
01110110 => [2,1,1,2,1,2] => 2
01110111 => [2,1,1,2,1,1,1] => 2
01111000 => [2,1,1,1,4] => 2
01111001 => [2,1,1,1,3,1] => 2
01111010 => [2,1,1,1,2,2] => 2
01111011 => [2,1,1,1,2,1,1] => 2
01111100 => [2,1,1,1,1,3] => 2
01111101 => [2,1,1,1,1,2,1] => 2
01111110 => [2,1,1,1,1,1,2] => 2
01111111 => [2,1,1,1,1,1,1,1] => 2
10000000 => [1,8] => 1
10000001 => [1,7,1] => 1
10000010 => [1,6,2] => 1
10000011 => [1,6,1,1] => 1
10000100 => [1,5,3] => 1
10000101 => [1,5,2,1] => 1
10000110 => [1,5,1,2] => 1
10000111 => [1,5,1,1,1] => 1
10001000 => [1,4,4] => 1
10001001 => [1,4,3,1] => 1
10001010 => [1,4,2,2] => 1
10001011 => [1,4,2,1,1] => 1
10001100 => [1,4,1,3] => 1
10001101 => [1,4,1,2,1] => 1
10001110 => [1,4,1,1,2] => 1
10001111 => [1,4,1,1,1,1] => 1
10010000 => [1,3,5] => 1
10010001 => [1,3,4,1] => 1
10010010 => [1,3,3,2] => 1
10010011 => [1,3,3,1,1] => 1
10010100 => [1,3,2,3] => 1
10010101 => [1,3,2,2,1] => 1
10010110 => [1,3,2,1,2] => 1
10010111 => [1,3,2,1,1,1] => 1
10011000 => [1,3,1,4] => 1
10011001 => [1,3,1,3,1] => 1
10011010 => [1,3,1,2,2] => 1
10011011 => [1,3,1,2,1,1] => 1
10011100 => [1,3,1,1,3] => 1
10011101 => [1,3,1,1,2,1] => 1
10011110 => [1,3,1,1,1,2] => 1
10011111 => [1,3,1,1,1,1,1] => 1
10100000 => [1,2,6] => 1
10100001 => [1,2,5,1] => 1
10100010 => [1,2,4,2] => 1
10100011 => [1,2,4,1,1] => 1
10100100 => [1,2,3,3] => 1
10100101 => [1,2,3,2,1] => 1
10100110 => [1,2,3,1,2] => 1
10100111 => [1,2,3,1,1,1] => 1
10101000 => [1,2,2,4] => 1
10101001 => [1,2,2,3,1] => 1
10101010 => [1,2,2,2,2] => 1
10101011 => [1,2,2,2,1,1] => 1
10101100 => [1,2,2,1,3] => 1
10101101 => [1,2,2,1,2,1] => 1
10101110 => [1,2,2,1,1,2] => 1
10101111 => [1,2,2,1,1,1,1] => 1
10110000 => [1,2,1,5] => 1
10110001 => [1,2,1,4,1] => 1
10110010 => [1,2,1,3,2] => 1
10110011 => [1,2,1,3,1,1] => 1
10110100 => [1,2,1,2,3] => 1
10110101 => [1,2,1,2,2,1] => 1
10110110 => [1,2,1,2,1,2] => 1
10110111 => [1,2,1,2,1,1,1] => 1
10111000 => [1,2,1,1,4] => 1
10111001 => [1,2,1,1,3,1] => 1
10111010 => [1,2,1,1,2,2] => 1
10111011 => [1,2,1,1,2,1,1] => 1
10111100 => [1,2,1,1,1,3] => 1
10111101 => [1,2,1,1,1,2,1] => 1
10111110 => [1,2,1,1,1,1,2] => 1
10111111 => [1,2,1,1,1,1,1,1] => 1
11000000 => [1,1,7] => 1
11000001 => [1,1,6,1] => 1
11000010 => [1,1,5,2] => 1
11000011 => [1,1,5,1,1] => 1
11000100 => [1,1,4,3] => 1
11000101 => [1,1,4,2,1] => 1
11000110 => [1,1,4,1,2] => 1
11000111 => [1,1,4,1,1,1] => 1
11001000 => [1,1,3,4] => 1
11001001 => [1,1,3,3,1] => 1
11001010 => [1,1,3,2,2] => 1
11001011 => [1,1,3,2,1,1] => 1
11001100 => [1,1,3,1,3] => 1
11001101 => [1,1,3,1,2,1] => 1
11001110 => [1,1,3,1,1,2] => 1
11001111 => [1,1,3,1,1,1,1] => 1
11010000 => [1,1,2,5] => 1
11010001 => [1,1,2,4,1] => 1
11010010 => [1,1,2,3,2] => 1
11010011 => [1,1,2,3,1,1] => 1
11010100 => [1,1,2,2,3] => 1
11010101 => [1,1,2,2,2,1] => 1
11010110 => [1,1,2,2,1,2] => 1
11010111 => [1,1,2,2,1,1,1] => 1
11011000 => [1,1,2,1,4] => 1
11011001 => [1,1,2,1,3,1] => 1
11011010 => [1,1,2,1,2,2] => 1
11011011 => [1,1,2,1,2,1,1] => 1
11011100 => [1,1,2,1,1,3] => 1
11011101 => [1,1,2,1,1,2,1] => 1
11011110 => [1,1,2,1,1,1,2] => 1
11011111 => [1,1,2,1,1,1,1,1] => 1
11100000 => [1,1,1,6] => 1
11100001 => [1,1,1,5,1] => 1
11100010 => [1,1,1,4,2] => 1
11100011 => [1,1,1,4,1,1] => 1
11100100 => [1,1,1,3,3] => 1
11100101 => [1,1,1,3,2,1] => 1
11100110 => [1,1,1,3,1,2] => 1
11100111 => [1,1,1,3,1,1,1] => 1
11101000 => [1,1,1,2,4] => 1
11101001 => [1,1,1,2,3,1] => 1
11101010 => [1,1,1,2,2,2] => 1
11101011 => [1,1,1,2,2,1,1] => 1
11101100 => [1,1,1,2,1,3] => 1
11101101 => [1,1,1,2,1,2,1] => 1
11101110 => [1,1,1,2,1,1,2] => 1
11101111 => [1,1,1,2,1,1,1,1] => 1
11110000 => [1,1,1,1,5] => 1
11110001 => [1,1,1,1,4,1] => 1
11110010 => [1,1,1,1,3,2] => 1
11110011 => [1,1,1,1,3,1,1] => 1
11110100 => [1,1,1,1,2,3] => 1
11110101 => [1,1,1,1,2,2,1] => 1
11110110 => [1,1,1,1,2,1,2] => 1
11110111 => [1,1,1,1,2,1,1,1] => 1
11111000 => [1,1,1,1,1,4] => 1
11111001 => [1,1,1,1,1,3,1] => 1
11111010 => [1,1,1,1,1,2,2] => 1
11111011 => [1,1,1,1,1,2,1,1] => 1
11111100 => [1,1,1,1,1,1,3] => 1
11111101 => [1,1,1,1,1,1,2,1] => 1
11111110 => [1,1,1,1,1,1,1,2] => 1
11111111 => [1,1,1,1,1,1,1,1,1] => 1
000000000 => [10] => 10
000000001 => [9,1] => 9
000000010 => [8,2] => 8
000000011 => [8,1,1] => 8
000000100 => [7,3] => 7
000000101 => [7,2,1] => 7
000000111 => [7,1,1,1] => 7
000001000 => [6,4] => 6
000001001 => [6,3,1] => 6
000001010 => [6,2,2] => 6
000001011 => [6,2,1,1] => 6
000001111 => [6,1,1,1,1] => 6
000010000 => [5,5] => 5
000010001 => [5,4,1] => 5
000010010 => [5,3,2] => 5
000010011 => [5,3,1,1] => 5
000010100 => [5,2,3] => 5
000010101 => [5,2,2,1] => 5
000010111 => [5,2,1,1,1] => 5
000011111 => [5,1,1,1,1,1] => 5
000100000 => [4,6] => 4
000100001 => [4,5,1] => 4
000100010 => [4,4,2] => 4
000100011 => [4,4,1,1] => 4
000100100 => [4,3,3] => 4
000100101 => [4,3,2,1] => 4
000100110 => [4,3,1,2] => 4
000100111 => [4,3,1,1,1] => 4
000101000 => [4,2,4] => 4
000101001 => [4,2,3,1] => 4
000101010 => [4,2,2,2] => 4
000101011 => [4,2,2,1,1] => 4
000101100 => [4,2,1,3] => 4
000101111 => [4,2,1,1,1,1] => 4
000110010 => [4,1,3,2] => 4
000110100 => [4,1,2,3] => 4
000111000 => [4,1,1,4] => 4
000111111 => [4,1,1,1,1,1,1] => 4
001000000 => [3,7] => 3
001000010 => [3,5,2] => 3
001000100 => [3,4,3] => 3
001000101 => [3,4,2,1] => 3
001000110 => [3,4,1,2] => 3
001001000 => [3,3,4] => 3
001001001 => [3,3,3,1] => 3
001001010 => [3,3,2,2] => 3
001001011 => [3,3,2,1,1] => 3
001001111 => [3,3,1,1,1,1] => 3
001010000 => [3,2,5] => 3
001010001 => [3,2,4,1] => 3
001010010 => [3,2,3,2] => 3
001010100 => [3,2,2,3] => 3
001010101 => [3,2,2,2,1] => 3
001010111 => [3,2,2,1,1,1] => 3
001011000 => [3,2,1,4] => 3
001011011 => [3,2,1,2,1,1] => 3
001011110 => [3,2,1,1,1,2] => 3
001011111 => [3,2,1,1,1,1,1] => 3
001100010 => [3,1,4,2] => 3
001100111 => [3,1,3,1,1,1] => 3
001101000 => [3,1,2,4] => 3
001110011 => [3,1,1,3,1,1] => 3
001110110 => [3,1,1,2,1,2] => 3
001111100 => [3,1,1,1,1,3] => 3
001111111 => [3,1,1,1,1,1,1,1] => 3
010000000 => [2,8] => 2
010000100 => [2,5,3] => 2
010001000 => [2,4,4] => 2
010001001 => [2,4,3,1] => 2
010001010 => [2,4,2,2] => 2
010001100 => [2,4,1,3] => 2
010010000 => [2,3,5] => 2
010010001 => [2,3,4,1] => 2
010010010 => [2,3,3,2] => 2
010010100 => [2,3,2,3] => 2
010010101 => [2,3,2,2,1] => 2
010011000 => [2,3,1,4] => 2
010100000 => [2,2,6] => 2
010100010 => [2,2,4,2] => 2
010100100 => [2,2,3,3] => 2
010100101 => [2,2,3,2,1] => 2
010101000 => [2,2,2,4] => 2
010101001 => [2,2,2,3,1] => 2
010101010 => [2,2,2,2,2] => 2
010101011 => [2,2,2,2,1,1] => 2
010101101 => [2,2,2,1,2,1] => 2
010101110 => [2,2,2,1,1,2] => 2
010101111 => [2,2,2,1,1,1,1] => 2
010110111 => [2,2,1,2,1,1,1] => 2
010111010 => [2,2,1,1,2,2] => 2
010111011 => [2,2,1,1,2,1,1] => 2
010111111 => [2,2,1,1,1,1,1,1] => 2
011000001 => [2,1,6,1] => 2
011000100 => [2,1,4,3] => 2
011001000 => [2,1,3,4] => 2
011010011 => [2,1,2,3,1,1] => 2
011010110 => [2,1,2,2,1,2] => 2
011010111 => [2,1,2,2,1,1,1] => 2
011011100 => [2,1,2,1,1,3] => 2
011011101 => [2,1,2,1,1,2,1] => 2
011101010 => [2,1,1,2,2,2] => 2
011101011 => [2,1,1,2,2,1,1] => 2
011101101 => [2,1,1,2,1,2,1] => 2
011101111 => [2,1,1,2,1,1,1,1] => 2
011110100 => [2,1,1,1,2,3] => 2
011111011 => [2,1,1,1,1,2,1,1] => 2
011111110 => [2,1,1,1,1,1,1,2] => 2
011111111 => [2,1,1,1,1,1,1,1,1] => 2
100000000 => [1,9] => 1
100000001 => [1,8,1] => 1
100000010 => [1,7,2] => 1
100000011 => [1,7,1,1] => 1
100000100 => [1,6,3] => 1
100000101 => [1,6,2,1] => 1
100000110 => [1,6,1,2] => 1
100001000 => [1,5,4] => 1
100001001 => [1,5,3,1] => 1
100001010 => [1,5,2,2] => 1
100001100 => [1,5,1,3] => 1
100001110 => [1,5,1,1,2] => 1
100001111 => [1,5,1,1,1,1] => 1
100010000 => [1,4,5] => 1
100010001 => [1,4,4,1] => 1
100010010 => [1,4,3,2] => 1
100010100 => [1,4,2,3] => 1
100010110 => [1,4,2,1,2] => 1
100011010 => [1,4,1,2,2] => 1
100011101 => [1,4,1,1,2,1] => 1
100011110 => [1,4,1,1,1,2] => 1
100100000 => [1,3,6] => 1
100100001 => [1,3,5,1] => 1
100100010 => [1,3,4,2] => 1
100100100 => [1,3,3,3] => 1
100100101 => [1,3,3,2,1] => 1
100100110 => [1,3,3,1,2] => 1
100101000 => [1,3,2,4] => 1
100101001 => [1,3,2,3,1] => 1
100101010 => [1,3,2,2,2] => 1
100101110 => [1,3,2,1,1,2] => 1
100110110 => [1,3,1,2,1,2] => 1
100110111 => [1,3,1,2,1,1,1] => 1
100111001 => [1,3,1,1,3,1] => 1
100111011 => [1,3,1,1,2,1,1] => 1
100111110 => [1,3,1,1,1,1,2] => 1
101000000 => [1,2,7] => 1
101000001 => [1,2,6,1] => 1
101000100 => [1,2,4,3] => 1
101001000 => [1,2,3,4] => 1
101001001 => [1,2,3,3,1] => 1
101001010 => [1,2,3,2,2] => 1
101001110 => [1,2,3,1,1,2] => 1
101010000 => [1,2,2,5] => 1
101010010 => [1,2,2,3,2] => 1
101010100 => [1,2,2,2,3] => 1
101010101 => [1,2,2,2,2,1] => 1
101011011 => [1,2,2,1,2,1,1] => 1
101011110 => [1,2,2,1,1,1,2] => 1
101100111 => [1,2,1,3,1,1,1] => 1
101101110 => [1,2,1,2,1,1,2] => 1
101110001 => [1,2,1,1,4,1] => 1
101110011 => [1,2,1,1,3,1,1] => 1
101110110 => [1,2,1,1,2,1,2] => 1
101111110 => [1,2,1,1,1,1,1,2] => 1
101111111 => [1,2,1,1,1,1,1,1,1] => 1
110000000 => [1,1,8] => 1
110000001 => [1,1,7,1] => 1
110001000 => [1,1,4,4] => 1
110010000 => [1,1,3,5] => 1
110010011 => [1,1,3,3,1,1] => 1
110010110 => [1,1,3,2,1,2] => 1
110010111 => [1,1,3,2,1,1,1] => 1
110011100 => [1,1,3,1,1,3] => 1
110011101 => [1,1,3,1,1,2,1] => 1
110011110 => [1,1,3,1,1,1,2] => 1
110100000 => [1,1,2,6] => 1
110100100 => [1,1,2,3,3] => 1
110100111 => [1,1,2,3,1,1,1] => 1
110101000 => [1,1,2,2,4] => 1
110101010 => [1,1,2,2,2,2] => 1
110101110 => [1,1,2,2,1,1,2] => 1
110101111 => [1,1,2,2,1,1,1,1] => 1
110110100 => [1,1,2,1,2,3] => 1
110111001 => [1,1,2,1,1,3,1] => 1
110111010 => [1,1,2,1,1,2,2] => 1
110111011 => [1,1,2,1,1,2,1,1] => 1
110111110 => [1,1,2,1,1,1,1,2] => 1
110111111 => [1,1,2,1,1,1,1,1,1] => 1
111000000 => [1,1,1,7] => 1
111001000 => [1,1,1,3,4] => 1
111001011 => [1,1,1,3,2,1,1] => 1
111001101 => [1,1,1,3,1,2,1] => 1
111010000 => [1,1,1,2,5] => 1
111010011 => [1,1,1,2,3,1,1] => 1
111010100 => [1,1,1,2,2,3] => 1
111010110 => [1,1,1,2,2,1,2] => 1
111011001 => [1,1,1,2,1,3,1] => 1
111011010 => [1,1,1,2,1,2,2] => 1
111011110 => [1,1,1,2,1,1,1,2] => 1
111011111 => [1,1,1,2,1,1,1,1,1] => 1
111100000 => [1,1,1,1,6] => 1
111100001 => [1,1,1,1,5,1] => 1
111100100 => [1,1,1,1,3,3] => 1
111101000 => [1,1,1,1,2,4] => 1
111101010 => [1,1,1,1,2,2,2] => 1
111101011 => [1,1,1,1,2,2,1,1] => 1
111101110 => [1,1,1,1,2,1,1,2] => 1
111101111 => [1,1,1,1,2,1,1,1,1] => 1
111110000 => [1,1,1,1,1,5] => 1
111110100 => [1,1,1,1,1,2,3] => 1
111110111 => [1,1,1,1,1,2,1,1,1] => 1
111111000 => [1,1,1,1,1,1,4] => 1
111111010 => [1,1,1,1,1,1,2,2] => 1
111111011 => [1,1,1,1,1,1,2,1,1] => 1
111111100 => [1,1,1,1,1,1,1,3] => 1
111111101 => [1,1,1,1,1,1,1,2,1] => 1
111111110 => [1,1,1,1,1,1,1,1,2] => 1
111111111 => [1,1,1,1,1,1,1,1,1,1] => 1
1010101010 => [1,2,2,2,2,2] => 1
1010101100 => [1,2,2,2,1,3] => 1
1010110010 => [1,2,2,1,3,2] => 1
1010110100 => [1,2,2,1,2,3] => 1
1010111000 => [1,2,2,1,1,4] => 1
1011001010 => [1,2,1,3,2,2] => 1
1011001100 => [1,2,1,3,1,3] => 1
1011010010 => [1,2,1,2,3,2] => 1
1011010100 => [1,2,1,2,2,3] => 1
1011011000 => [1,2,1,2,1,4] => 1
1011100010 => [1,2,1,1,4,2] => 1
1011100100 => [1,2,1,1,3,3] => 1
1011101000 => [1,2,1,1,2,4] => 1
1011110000 => [1,2,1,1,1,5] => 1
1100101010 => [1,1,3,2,2,2] => 1
1100101100 => [1,1,3,2,1,3] => 1
1100110010 => [1,1,3,1,3,2] => 1
1100110100 => [1,1,3,1,2,3] => 1
1100111000 => [1,1,3,1,1,4] => 1
1101001010 => [1,1,2,3,2,2] => 1
1101001100 => [1,1,2,3,1,3] => 1
1101010010 => [1,1,2,2,3,2] => 1
1101010100 => [1,1,2,2,2,3] => 1
1101011000 => [1,1,2,2,1,4] => 1
1101100010 => [1,1,2,1,4,2] => 1
1101100100 => [1,1,2,1,3,3] => 1
1101101000 => [1,1,2,1,2,4] => 1
1101110000 => [1,1,2,1,1,5] => 1
1110001010 => [1,1,1,4,2,2] => 1
1110001100 => [1,1,1,4,1,3] => 1
1110010010 => [1,1,1,3,3,2] => 1
1110010100 => [1,1,1,3,2,3] => 1
1110011000 => [1,1,1,3,1,4] => 1
1110100010 => [1,1,1,2,4,2] => 1
1110100100 => [1,1,1,2,3,3] => 1
1110101000 => [1,1,1,2,2,4] => 1
1110110000 => [1,1,1,2,1,5] => 1
1111000010 => [1,1,1,1,5,2] => 1
1111000100 => [1,1,1,1,4,3] => 1
1111001000 => [1,1,1,1,3,4] => 1
1111010000 => [1,1,1,1,2,5] => 1
1111100000 => [1,1,1,1,1,6] => 1
101010101010 => [1,2,2,2,2,2,2] => 1
101010101100 => [1,2,2,2,2,1,3] => 1
101010110010 => [1,2,2,2,1,3,2] => 1
101010110100 => [1,2,2,2,1,2,3] => 1
101010111000 => [1,2,2,2,1,1,4] => 1
101011001010 => [1,2,2,1,3,2,2] => 1
101011001100 => [1,2,2,1,3,1,3] => 1
101011010010 => [1,2,2,1,2,3,2] => 1
101011010100 => [1,2,2,1,2,2,3] => 1
101011011000 => [1,2,2,1,2,1,4] => 1
101011100010 => [1,2,2,1,1,4,2] => 1
101011100100 => [1,2,2,1,1,3,3] => 1
101011101000 => [1,2,2,1,1,2,4] => 1
101011110000 => [1,2,2,1,1,1,5] => 1
101100101010 => [1,2,1,3,2,2,2] => 1
101100101100 => [1,2,1,3,2,1,3] => 1
101100110010 => [1,2,1,3,1,3,2] => 1
101100110100 => [1,2,1,3,1,2,3] => 1
101100111000 => [1,2,1,3,1,1,4] => 1
101101001010 => [1,2,1,2,3,2,2] => 1
101101001100 => [1,2,1,2,3,1,3] => 1
101101010010 => [1,2,1,2,2,3,2] => 1
101101010100 => [1,2,1,2,2,2,3] => 1
101101011000 => [1,2,1,2,2,1,4] => 1
101101100010 => [1,2,1,2,1,4,2] => 1
101101100100 => [1,2,1,2,1,3,3] => 1
101101101000 => [1,2,1,2,1,2,4] => 1
101101110000 => [1,2,1,2,1,1,5] => 1
101110001010 => [1,2,1,1,4,2,2] => 1
101110001100 => [1,2,1,1,4,1,3] => 1
101110010010 => [1,2,1,1,3,3,2] => 1
101110010100 => [1,2,1,1,3,2,3] => 1
101110011000 => [1,2,1,1,3,1,4] => 1
101110100010 => [1,2,1,1,2,4,2] => 1
101110100100 => [1,2,1,1,2,3,3] => 1
101110101000 => [1,2,1,1,2,2,4] => 1
101110110000 => [1,2,1,1,2,1,5] => 1
101111000010 => [1,2,1,1,1,5,2] => 1
101111000100 => [1,2,1,1,1,4,3] => 1
101111001000 => [1,2,1,1,1,3,4] => 1
101111010000 => [1,2,1,1,1,2,5] => 1
101111100000 => [1,2,1,1,1,1,6] => 1
110010101010 => [1,1,3,2,2,2,2] => 1
110010101100 => [1,1,3,2,2,1,3] => 1
110010110010 => [1,1,3,2,1,3,2] => 1
110010110100 => [1,1,3,2,1,2,3] => 1
110010111000 => [1,1,3,2,1,1,4] => 1
110011001010 => [1,1,3,1,3,2,2] => 1
110011001100 => [1,1,3,1,3,1,3] => 1
110011010010 => [1,1,3,1,2,3,2] => 1
110011010100 => [1,1,3,1,2,2,3] => 1
110011011000 => [1,1,3,1,2,1,4] => 1
110011100010 => [1,1,3,1,1,4,2] => 1
110011100100 => [1,1,3,1,1,3,3] => 1
110011101000 => [1,1,3,1,1,2,4] => 1
110011110000 => [1,1,3,1,1,1,5] => 1
110100101010 => [1,1,2,3,2,2,2] => 1
110100101100 => [1,1,2,3,2,1,3] => 1
110100110010 => [1,1,2,3,1,3,2] => 1
110100110100 => [1,1,2,3,1,2,3] => 1
110100111000 => [1,1,2,3,1,1,4] => 1
110101001010 => [1,1,2,2,3,2,2] => 1
110101001100 => [1,1,2,2,3,1,3] => 1
110101010010 => [1,1,2,2,2,3,2] => 1
110101010100 => [1,1,2,2,2,2,3] => 1
110101011000 => [1,1,2,2,2,1,4] => 1
110101100010 => [1,1,2,2,1,4,2] => 1
110101100100 => [1,1,2,2,1,3,3] => 1
110101101000 => [1,1,2,2,1,2,4] => 1
110101110000 => [1,1,2,2,1,1,5] => 1
110110001010 => [1,1,2,1,4,2,2] => 1
110110001100 => [1,1,2,1,4,1,3] => 1
110110010010 => [1,1,2,1,3,3,2] => 1
110110010100 => [1,1,2,1,3,2,3] => 1
110110011000 => [1,1,2,1,3,1,4] => 1
110110100010 => [1,1,2,1,2,4,2] => 1
110110100100 => [1,1,2,1,2,3,3] => 1
110110101000 => [1,1,2,1,2,2,4] => 1
110110110000 => [1,1,2,1,2,1,5] => 1
110111000010 => [1,1,2,1,1,5,2] => 1
110111000100 => [1,1,2,1,1,4,3] => 1
110111001000 => [1,1,2,1,1,3,4] => 1
110111010000 => [1,1,2,1,1,2,5] => 1
110111100000 => [1,1,2,1,1,1,6] => 1
111000101010 => [1,1,1,4,2,2,2] => 1
111000101100 => [1,1,1,4,2,1,3] => 1
111000110010 => [1,1,1,4,1,3,2] => 1
111000110100 => [1,1,1,4,1,2,3] => 1
111000111000 => [1,1,1,4,1,1,4] => 1
111001001010 => [1,1,1,3,3,2,2] => 1
111001001100 => [1,1,1,3,3,1,3] => 1
111001010010 => [1,1,1,3,2,3,2] => 1
111001010100 => [1,1,1,3,2,2,3] => 1
111001011000 => [1,1,1,3,2,1,4] => 1
111001100010 => [1,1,1,3,1,4,2] => 1
111001100100 => [1,1,1,3,1,3,3] => 1
111001101000 => [1,1,1,3,1,2,4] => 1
111001110000 => [1,1,1,3,1,1,5] => 1
111010001010 => [1,1,1,2,4,2,2] => 1
111010001100 => [1,1,1,2,4,1,3] => 1
111010010010 => [1,1,1,2,3,3,2] => 1
111010010100 => [1,1,1,2,3,2,3] => 1
111010011000 => [1,1,1,2,3,1,4] => 1
111010100010 => [1,1,1,2,2,4,2] => 1
111010100100 => [1,1,1,2,2,3,3] => 1
111010101000 => [1,1,1,2,2,2,4] => 1
111010110000 => [1,1,1,2,2,1,5] => 1
111011000010 => [1,1,1,2,1,5,2] => 1
111011000100 => [1,1,1,2,1,4,3] => 1
111011001000 => [1,1,1,2,1,3,4] => 1
111011010000 => [1,1,1,2,1,2,5] => 1
111011100000 => [1,1,1,2,1,1,6] => 1
111100001010 => [1,1,1,1,5,2,2] => 1
111100001100 => [1,1,1,1,5,1,3] => 1
111100010010 => [1,1,1,1,4,3,2] => 1
111100010100 => [1,1,1,1,4,2,3] => 1
111100011000 => [1,1,1,1,4,1,4] => 1
111100100010 => [1,1,1,1,3,4,2] => 1
111100100100 => [1,1,1,1,3,3,3] => 1
111100101000 => [1,1,1,1,3,2,4] => 1
111100110000 => [1,1,1,1,3,1,5] => 1
111101000010 => [1,1,1,1,2,5,2] => 1
111101000100 => [1,1,1,1,2,4,3] => 1
111101001000 => [1,1,1,1,2,3,4] => 1
111101010000 => [1,1,1,1,2,2,5] => 1
111101100000 => [1,1,1,1,2,1,6] => 1
111110000010 => [1,1,1,1,1,6,2] => 1
111110000100 => [1,1,1,1,1,5,3] => 1
111110001000 => [1,1,1,1,1,4,4] => 1
111110010000 => [1,1,1,1,1,3,5] => 1
111110100000 => [1,1,1,1,1,2,6] => 1
111111000000 => [1,1,1,1,1,1,7] => 1
1111111111 => [1,1,1,1,1,1,1,1,1,1,1] => 1
1111111110 => [1,1,1,1,1,1,1,1,1,2] => 1
1101111110 => [1,1,2,1,1,1,1,1,2] => 1
1100000001 => [1,1,8,1] => 1
1011111110 => [1,2,1,1,1,1,1,1,2] => 1
1010111110 => [1,2,2,1,1,1,1,2] => 1
1010000001 => [1,2,7,1] => 1
1001111110 => [1,3,1,1,1,1,1,2] => 1
1001011110 => [1,3,2,1,1,1,2] => 1
1000111110 => [1,4,1,1,1,1,2] => 1
1000101110 => [1,4,2,1,1,2] => 1
1000011110 => [1,5,1,1,1,2] => 1
1000010110 => [1,5,2,1,2] => 1
1000001110 => [1,6,1,1,2] => 1
1000001010 => [1,6,2,2] => 1
1000001001 => [1,6,3,1] => 1
1000000110 => [1,7,1,2] => 1
1000000101 => [1,7,2,1] => 1
1000000100 => [1,7,3] => 1
1000000011 => [1,8,1,1] => 1
1000000010 => [1,8,2] => 1
1000000000 => [1,10] => 1
10000000000 => [1,11] => 1
10000000010 => [1,9,2] => 1
10000000110 => [1,8,1,2] => 1
10000001110 => [1,7,1,1,2] => 1
10000011110 => [1,6,1,1,1,2] => 1
10000111110 => [1,5,1,1,1,1,2] => 1
10001111110 => [1,4,1,1,1,1,1,2] => 1
10011111110 => [1,3,1,1,1,1,1,1,2] => 1
10111111110 => [1,2,1,1,1,1,1,1,1,2] => 1
11111111110 => [1,1,1,1,1,1,1,1,1,1,2] => 1
11011111110 => [1,1,2,1,1,1,1,1,1,2] => 1
10000010000 => [1,6,5] => 1
10000100010 => [1,5,4,2] => 1
11110111110 => [1,1,1,1,2,1,1,1,1,2] => 1
10001000010 => [1,4,5,2] => 1
10000100100 => [1,5,3,3] => 1
10001001010 => [1,4,3,2,2] => 1
10001000100 => [1,4,4,3] => 1
10000101000 => [1,5,2,4] => 1
10010001010 => [1,3,4,2,2] => 1
10001010010 => [1,4,2,3,2] => 1
11111101110 => [1,1,1,1,1,1,2,1,1,2] => 1
10010000100 => [1,3,5,3] => 1
10001001000 => [1,4,3,4] => 1
10010010010 => [1,3,3,3,2] => 1
10001010100 => [1,4,2,2,3] => 1
10010101010 => [1,3,2,2,2,2] => 1
11010101110 => [1,1,2,2,2,1,1,2] => 1
10010001000 => [1,3,4,4] => 1
10100010010 => [1,2,4,3,2] => 1
10010100010 => [1,3,2,4,2] => 1
10010010100 => [1,3,3,2,3] => 1
10100101010 => [1,2,3,2,2,2] => 1
11111111010 => [1,1,1,1,1,1,1,1,2,2] => 1
=> [1] => 1
0000000001 => [10,1] => 10
11010100100 => [1,1,2,2,3,3] => 1
11001010100 => [1,1,3,2,2,3] => 1
00101010101 => [3,2,2,2,2,1] => 3
00101010011 => [3,2,2,3,1,1] => 3
00100101011 => [3,3,2,2,1,1] => 3
01111111110 => [2,1,1,1,1,1,1,1,1,2] => 2
10101010101 => [1,2,2,2,2,2,1] => 1
10101010010 => [1,2,2,2,3,2] => 1
10101001001 => [1,2,2,3,3,1] => 1
10101001010 => [1,2,2,3,2,2] => 1
10101000100 => [1,2,2,4,3] => 1
10100100101 => [1,2,3,3,2,1] => 1
10100100010 => [1,2,3,4,2] => 1
10100101001 => [1,2,3,2,3,1] => 1
10100100100 => [1,2,3,3,3] => 1
10100010001 => [1,2,4,4,1] => 1
10100010100 => [1,2,4,2,3] => 1
10100001000 => [1,2,5,4] => 1
10010010101 => [1,3,3,2,2,1] => 1
10010001001 => [1,3,4,3,1] => 1
10010100101 => [1,3,2,3,2,1] => 1
10010101001 => [1,3,2,2,3,1] => 1
10010100100 => [1,3,2,3,3] => 1
10010010001 => [1,3,3,4,1] => 1
10001000101 => [1,4,4,2,1] => 1
10001001001 => [1,4,3,3,1] => 1
10001010001 => [1,4,2,4,1] => 1
10000100001 => [1,5,5,1] => 1
01001010101 => [2,3,2,2,2,1] => 2
01001010010 => [2,3,2,3,2] => 2
01001001001 => [2,3,3,3,1] => 2
01001001010 => [2,3,3,2,2] => 2
01001000100 => [2,3,4,3] => 2
01000100101 => [2,4,3,2,1] => 2
01000100010 => [2,4,4,2] => 2
01000101001 => [2,4,2,3,1] => 2
01000101010 => [2,4,2,2,2] => 2
01000100100 => [2,4,3,3] => 2
01000010001 => [2,5,4,1] => 2
01000010010 => [2,5,3,2] => 2
01000010100 => [2,5,2,3] => 2
01000001000 => [2,6,4] => 2
01010010101 => [2,2,3,2,2,1] => 2
01010010010 => [2,2,3,3,2] => 2
01010001001 => [2,2,4,3,1] => 2
01010001010 => [2,2,4,2,2] => 2
01010000100 => [2,2,5,3] => 2
01010100101 => [2,2,2,3,2,1] => 2
01010100010 => [2,2,2,4,2] => 2
01010101001 => [2,2,2,2,3,1] => 2
01010101010 => [2,2,2,2,2,2] => 2
01010100100 => [2,2,2,3,3] => 2
01010010001 => [2,2,3,4,1] => 2
01010010100 => [2,2,3,2,3] => 2
01010001000 => [2,2,4,4] => 2
01001000101 => [2,3,4,2,1] => 2
01001000010 => [2,3,5,2] => 2
01001010001 => [2,3,2,4,1] => 2
01001010100 => [2,3,2,2,3] => 2
01001001000 => [2,3,3,4] => 2
01000100001 => [2,4,5,1] => 2
01000101000 => [2,4,2,4] => 2
01000010000 => [2,5,5] => 2
00100010101 => [3,4,2,2,1] => 3
00100010010 => [3,4,3,2] => 3
00100001001 => [3,5,3,1] => 3
00100001010 => [3,5,2,2] => 3
00100000100 => [3,6,3] => 3
00100100101 => [3,3,3,2,1] => 3
00100100010 => [3,3,4,2] => 3
00100101001 => [3,3,2,3,1] => 3
00100101010 => [3,3,2,2,2] => 3
00100100100 => [3,3,3,3] => 3
00100010001 => [3,4,4,1] => 3
00100010100 => [3,4,2,3] => 3
00100001000 => [3,5,4] => 3
00101000101 => [3,2,4,2,1] => 3
00101000010 => [3,2,5,2] => 3
00101001001 => [3,2,3,3,1] => 3
00101001010 => [3,2,3,2,2] => 3
00101000100 => [3,2,4,3] => 3
00101010001 => [3,2,2,4,1] => 3
00101010010 => [3,2,2,3,2] => 3
00101010100 => [3,2,2,2,3] => 3
00101001000 => [3,2,3,4] => 3
00100100001 => [3,3,5,1] => 3
00100101000 => [3,3,2,4] => 3
00100010000 => [3,4,5] => 3
00010000101 => [4,5,2,1] => 4
00010000010 => [4,6,2] => 4
00010001001 => [4,4,3,1] => 4
00010001010 => [4,4,2,2] => 4
00010000100 => [4,5,3] => 4
00010010001 => [4,3,4,1] => 4
00010010010 => [4,3,3,2] => 4
00010010100 => [4,3,2,3] => 4
00010001000 => [4,4,4] => 4
00010100001 => [4,2,5,1] => 4
00010100010 => [4,2,4,2] => 4
00010100100 => [4,2,3,3] => 4
00010101000 => [4,2,2,4] => 4
00010010000 => [4,3,5] => 4
00001000001 => [5,6,1] => 5
00001000010 => [5,5,2] => 5
00001000100 => [5,4,3] => 5
00001001000 => [5,3,4] => 5
00001010000 => [5,2,5] => 5
00000100000 => [6,6] => 6
01011111111 => [2,2,1,1,1,1,1,1,1,1] => 2
01111111011 => [2,1,1,1,1,1,1,2,1,1] => 2
11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
01010111011 => [2,2,2,1,1,2,1,1] => 2
01011101110 => [2,2,1,1,2,1,1,2] => 2
01011101011 => [2,2,1,1,2,2,1,1] => 2
01101110110 => [2,1,2,1,1,2,1,2] => 2
01101011011 => [2,1,2,2,1,2,1,1] => 2
01110111010 => [2,1,1,2,1,1,2,2] => 2
01110101110 => [2,1,1,2,2,1,1,2] => 2
01110101011 => [2,1,1,2,2,2,1,1] => 2
01111101111 => [2,1,1,1,1,2,1,1,1,1] => 2
11011101010 => [1,1,2,1,1,2,2,2] => 1
11011111011 => [1,1,2,1,1,1,1,2,1,1] => 1
11011010110 => [1,1,2,1,2,2,1,2] => 1
11010111010 => [1,1,2,2,1,1,2,2] => 1
11010101011 => [1,1,2,2,2,2,1,1] => 1
11011101111 => [1,1,2,1,1,2,1,1,1,1] => 1
11110111011 => [1,1,1,1,2,1,1,2,1,1] => 1
11110101111 => [1,1,1,1,2,2,1,1,1,1] => 1
0001000100 => [4,4,3] => 4
00101111110 => [3,2,1,1,1,1,1,2] => 3
00111011110 => [3,1,1,2,1,1,1,2] => 3
00111110110 => [3,1,1,1,1,2,1,2] => 3
00111111100 => [3,1,1,1,1,1,1,3] => 3
00010010101 => [4,3,2,2,1] => 4
00010100101 => [4,2,3,2,1] => 4
00010101001 => [4,2,2,3,1] => 4
00010101010 => [4,2,2,2,2] => 4
00000100010 => [6,4,2] => 6
01101010100 => [2,1,2,2,2,3] => 2
01101001010 => [2,1,2,3,2,2] => 2
01010101111 => [2,2,2,2,1,1,1,1] => 2
11011110100 => [1,1,2,1,1,1,2,3] => 1
01010110100 => [2,2,2,1,2,3] => 2
01110111111 => [2,1,1,2,1,1,1,1,1,1] => 2
11110001000 => [1,1,1,1,4,4] => 1
11000111000 => [1,1,4,1,1,4] => 1
11000100011 => [1,1,4,4,1,1] => 1
00011111000 => [4,1,1,1,1,4] => 4
00011100011 => [4,1,1,4,1,1] => 4
00010001111 => [4,4,1,1,1,1] => 4
01011111010 => [2,2,1,1,1,1,2,2] => 2
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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:
1,1 2,1,1 4,2,1,1 8,4,2,1,1 16,8,4,2,1,1 32,16,8,4,2,1,1 64,32,16,8,4,2,1,1 128,64,32,16,8,4,2,1,1
$F_{1} = q + q^{2}$
$F_{2} = 2\ q + q^{2} + q^{3}$
$F_{3} = 4\ q + 2\ q^{2} + q^{3} + q^{4}$
$F_{4} = 8\ q + 4\ q^{2} + 2\ q^{3} + q^{4} + q^{5}$
$F_{5} = 16\ q + 8\ q^{2} + 4\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{6} = 32\ q + 16\ q^{2} + 8\ q^{3} + 4\ q^{4} + 2\ q^{5} + q^{6} + q^{7}$
$F_{7} = 64\ q + 32\ q^{2} + 16\ q^{3} + 8\ q^{4} + 4\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$
$F_{8} = 128\ q + 64\ q^{2} + 32\ q^{3} + 16\ q^{4} + 8\ q^{5} + 4\ q^{6} + 2\ q^{7} + q^{8} + q^{9}$
Description
The first part of an integer composition.
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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