Identifier
-
Mp00104:
Binary words
—reverse⟶
Binary words
St000391: Binary words ⟶ ℤ
Values
0 => 0 => 0
1 => 1 => 1
00 => 00 => 0
01 => 10 => 1
10 => 01 => 2
11 => 11 => 3
000 => 000 => 0
001 => 100 => 1
010 => 010 => 2
011 => 110 => 3
100 => 001 => 3
101 => 101 => 4
110 => 011 => 5
111 => 111 => 6
0000 => 0000 => 0
0001 => 1000 => 1
0010 => 0100 => 2
0011 => 1100 => 3
0100 => 0010 => 3
0101 => 1010 => 4
0110 => 0110 => 5
0111 => 1110 => 6
1000 => 0001 => 4
1001 => 1001 => 5
1010 => 0101 => 6
1011 => 1101 => 7
1100 => 0011 => 7
1101 => 1011 => 8
1110 => 0111 => 9
1111 => 1111 => 10
00000 => 00000 => 0
00001 => 10000 => 1
00010 => 01000 => 2
00011 => 11000 => 3
00100 => 00100 => 3
00101 => 10100 => 4
00110 => 01100 => 5
00111 => 11100 => 6
01000 => 00010 => 4
01001 => 10010 => 5
01010 => 01010 => 6
01011 => 11010 => 7
01100 => 00110 => 7
01101 => 10110 => 8
01110 => 01110 => 9
01111 => 11110 => 10
10000 => 00001 => 5
10001 => 10001 => 6
10010 => 01001 => 7
10011 => 11001 => 8
10100 => 00101 => 8
10101 => 10101 => 9
10110 => 01101 => 10
10111 => 11101 => 11
11000 => 00011 => 9
11001 => 10011 => 10
11010 => 01011 => 11
11011 => 11011 => 12
11100 => 00111 => 12
11101 => 10111 => 13
11110 => 01111 => 14
11111 => 11111 => 15
000000 => 000000 => 0
000001 => 100000 => 1
000010 => 010000 => 2
000011 => 110000 => 3
000100 => 001000 => 3
000101 => 101000 => 4
000110 => 011000 => 5
000111 => 111000 => 6
001000 => 000100 => 4
001001 => 100100 => 5
001010 => 010100 => 6
001011 => 110100 => 7
001100 => 001100 => 7
001101 => 101100 => 8
001110 => 011100 => 9
001111 => 111100 => 10
010000 => 000010 => 5
010001 => 100010 => 6
010010 => 010010 => 7
010011 => 110010 => 8
010100 => 001010 => 8
010101 => 101010 => 9
010110 => 011010 => 10
010111 => 111010 => 11
011000 => 000110 => 9
011001 => 100110 => 10
011010 => 010110 => 11
011011 => 110110 => 12
011100 => 001110 => 12
011101 => 101110 => 13
011110 => 011110 => 14
011111 => 111110 => 15
100000 => 000001 => 6
100001 => 100001 => 7
100010 => 010001 => 8
100011 => 110001 => 9
100100 => 001001 => 9
100101 => 101001 => 10
100110 => 011001 => 11
>>> Load all 1191 entries. <<<100111 => 111001 => 12
101000 => 000101 => 10
101001 => 100101 => 11
101010 => 010101 => 12
101011 => 110101 => 13
101100 => 001101 => 13
101101 => 101101 => 14
101110 => 011101 => 15
101111 => 111101 => 16
110000 => 000011 => 11
110001 => 100011 => 12
110010 => 010011 => 13
110011 => 110011 => 14
110100 => 001011 => 14
110101 => 101011 => 15
110110 => 011011 => 16
110111 => 111011 => 17
111000 => 000111 => 15
111001 => 100111 => 16
111010 => 010111 => 17
111011 => 110111 => 18
111100 => 001111 => 18
111101 => 101111 => 19
111110 => 011111 => 20
111111 => 111111 => 21
0000000 => 0000000 => 0
0000001 => 1000000 => 1
0000010 => 0100000 => 2
0000011 => 1100000 => 3
0000100 => 0010000 => 3
0000101 => 1010000 => 4
0000110 => 0110000 => 5
0000111 => 1110000 => 6
0001000 => 0001000 => 4
0001001 => 1001000 => 5
0001010 => 0101000 => 6
0001011 => 1101000 => 7
0001100 => 0011000 => 7
0001101 => 1011000 => 8
0001110 => 0111000 => 9
0001111 => 1111000 => 10
0010000 => 0000100 => 5
0010001 => 1000100 => 6
0010010 => 0100100 => 7
0010011 => 1100100 => 8
0010100 => 0010100 => 8
0010101 => 1010100 => 9
0010110 => 0110100 => 10
0010111 => 1110100 => 11
0011000 => 0001100 => 9
0011001 => 1001100 => 10
0011010 => 0101100 => 11
0011011 => 1101100 => 12
0011100 => 0011100 => 12
0011101 => 1011100 => 13
0011110 => 0111100 => 14
0011111 => 1111100 => 15
0100000 => 0000010 => 6
0100001 => 1000010 => 7
0100010 => 0100010 => 8
0100011 => 1100010 => 9
0100100 => 0010010 => 9
0100101 => 1010010 => 10
0100110 => 0110010 => 11
0100111 => 1110010 => 12
0101000 => 0001010 => 10
0101001 => 1001010 => 11
0101010 => 0101010 => 12
0101011 => 1101010 => 13
0101100 => 0011010 => 13
0101101 => 1011010 => 14
0101110 => 0111010 => 15
0101111 => 1111010 => 16
0110000 => 0000110 => 11
0110001 => 1000110 => 12
0110010 => 0100110 => 13
0110011 => 1100110 => 14
0110100 => 0010110 => 14
0110101 => 1010110 => 15
0110110 => 0110110 => 16
0110111 => 1110110 => 17
0111000 => 0001110 => 15
0111001 => 1001110 => 16
0111010 => 0101110 => 17
0111011 => 1101110 => 18
0111100 => 0011110 => 18
0111101 => 1011110 => 19
0111110 => 0111110 => 20
0111111 => 1111110 => 21
1000000 => 0000001 => 7
1000001 => 1000001 => 8
1000010 => 0100001 => 9
1000011 => 1100001 => 10
1000100 => 0010001 => 10
1000101 => 1010001 => 11
1000110 => 0110001 => 12
1000111 => 1110001 => 13
1001000 => 0001001 => 11
1001001 => 1001001 => 12
1001010 => 0101001 => 13
1001011 => 1101001 => 14
1001100 => 0011001 => 14
1001101 => 1011001 => 15
1001110 => 0111001 => 16
1001111 => 1111001 => 17
1010000 => 0000101 => 12
1010001 => 1000101 => 13
1010010 => 0100101 => 14
1010011 => 1100101 => 15
1010100 => 0010101 => 15
1010101 => 1010101 => 16
1010110 => 0110101 => 17
1010111 => 1110101 => 18
1011000 => 0001101 => 16
1011001 => 1001101 => 17
1011010 => 0101101 => 18
1011011 => 1101101 => 19
1011100 => 0011101 => 19
1011101 => 1011101 => 20
1011110 => 0111101 => 21
1011111 => 1111101 => 22
1100000 => 0000011 => 13
1100001 => 1000011 => 14
1100010 => 0100011 => 15
1100011 => 1100011 => 16
1100100 => 0010011 => 16
1100101 => 1010011 => 17
1100110 => 0110011 => 18
1100111 => 1110011 => 19
1101000 => 0001011 => 17
1101001 => 1001011 => 18
1101010 => 0101011 => 19
1101011 => 1101011 => 20
1101100 => 0011011 => 20
1101101 => 1011011 => 21
1101110 => 0111011 => 22
1101111 => 1111011 => 23
1110000 => 0000111 => 18
1110001 => 1000111 => 19
1110010 => 0100111 => 20
1110011 => 1100111 => 21
1110100 => 0010111 => 21
1110101 => 1010111 => 22
1110110 => 0110111 => 23
1110111 => 1110111 => 24
1111000 => 0001111 => 22
1111001 => 1001111 => 23
1111010 => 0101111 => 24
1111011 => 1101111 => 25
1111100 => 0011111 => 25
1111101 => 1011111 => 26
1111110 => 0111111 => 27
1111111 => 1111111 => 28
00000000 => 00000000 => 0
00000001 => 10000000 => 1
00000010 => 01000000 => 2
00000011 => 11000000 => 3
00000100 => 00100000 => 3
00000101 => 10100000 => 4
00000110 => 01100000 => 5
00000111 => 11100000 => 6
00001000 => 00010000 => 4
00001001 => 10010000 => 5
00001010 => 01010000 => 6
00001011 => 11010000 => 7
00001100 => 00110000 => 7
00001101 => 10110000 => 8
00001110 => 01110000 => 9
00001111 => 11110000 => 10
00010000 => 00001000 => 5
00010001 => 10001000 => 6
00010010 => 01001000 => 7
00010011 => 11001000 => 8
00010100 => 00101000 => 8
00010101 => 10101000 => 9
00010110 => 01101000 => 10
00010111 => 11101000 => 11
00011000 => 00011000 => 9
00011001 => 10011000 => 10
00011010 => 01011000 => 11
00011011 => 11011000 => 12
00011100 => 00111000 => 12
00011101 => 10111000 => 13
00011110 => 01111000 => 14
00011111 => 11111000 => 15
00100000 => 00000100 => 6
00100001 => 10000100 => 7
00100010 => 01000100 => 8
00100011 => 11000100 => 9
00100100 => 00100100 => 9
00100101 => 10100100 => 10
00100110 => 01100100 => 11
00100111 => 11100100 => 12
00101000 => 00010100 => 10
00101001 => 10010100 => 11
00101010 => 01010100 => 12
00101011 => 11010100 => 13
00101100 => 00110100 => 13
00101101 => 10110100 => 14
00101110 => 01110100 => 15
00101111 => 11110100 => 16
00110000 => 00001100 => 11
00110001 => 10001100 => 12
00110010 => 01001100 => 13
00110011 => 11001100 => 14
00110100 => 00101100 => 14
00110101 => 10101100 => 15
00110110 => 01101100 => 16
00110111 => 11101100 => 17
00111000 => 00011100 => 15
00111001 => 10011100 => 16
00111010 => 01011100 => 17
00111011 => 11011100 => 18
00111100 => 00111100 => 18
00111101 => 10111100 => 19
00111110 => 01111100 => 20
00111111 => 11111100 => 21
01000000 => 00000010 => 7
01000001 => 10000010 => 8
01000010 => 01000010 => 9
01000011 => 11000010 => 10
01000100 => 00100010 => 10
01000101 => 10100010 => 11
01000110 => 01100010 => 12
01000111 => 11100010 => 13
01001000 => 00010010 => 11
01001001 => 10010010 => 12
01001010 => 01010010 => 13
01001011 => 11010010 => 14
01001100 => 00110010 => 14
01001101 => 10110010 => 15
01001110 => 01110010 => 16
01001111 => 11110010 => 17
01010000 => 00001010 => 12
01010001 => 10001010 => 13
01010010 => 01001010 => 14
01010011 => 11001010 => 15
01010100 => 00101010 => 15
01010101 => 10101010 => 16
01010110 => 01101010 => 17
01010111 => 11101010 => 18
01011000 => 00011010 => 16
01011001 => 10011010 => 17
01011010 => 01011010 => 18
01011011 => 11011010 => 19
01011100 => 00111010 => 19
01011101 => 10111010 => 20
01011110 => 01111010 => 21
01011111 => 11111010 => 22
01100000 => 00000110 => 13
01100001 => 10000110 => 14
01100010 => 01000110 => 15
01100011 => 11000110 => 16
01100100 => 00100110 => 16
01100101 => 10100110 => 17
01100110 => 01100110 => 18
01100111 => 11100110 => 19
01101000 => 00010110 => 17
01101001 => 10010110 => 18
01101010 => 01010110 => 19
01101011 => 11010110 => 20
01101100 => 00110110 => 20
01101101 => 10110110 => 21
01101110 => 01110110 => 22
01101111 => 11110110 => 23
01110000 => 00001110 => 18
01110001 => 10001110 => 19
01110010 => 01001110 => 20
01110011 => 11001110 => 21
01110100 => 00101110 => 21
01110101 => 10101110 => 22
01110110 => 01101110 => 23
01110111 => 11101110 => 24
01111000 => 00011110 => 22
01111001 => 10011110 => 23
01111010 => 01011110 => 24
01111011 => 11011110 => 25
01111100 => 00111110 => 25
01111101 => 10111110 => 26
01111110 => 01111110 => 27
01111111 => 11111110 => 28
10000000 => 00000001 => 8
10000001 => 10000001 => 9
10000010 => 01000001 => 10
10000011 => 11000001 => 11
10000100 => 00100001 => 11
10000101 => 10100001 => 12
10000110 => 01100001 => 13
10000111 => 11100001 => 14
10001000 => 00010001 => 12
10001001 => 10010001 => 13
10001010 => 01010001 => 14
10001011 => 11010001 => 15
10001100 => 00110001 => 15
10001101 => 10110001 => 16
10001110 => 01110001 => 17
10001111 => 11110001 => 18
10010000 => 00001001 => 13
10010001 => 10001001 => 14
10010010 => 01001001 => 15
10010011 => 11001001 => 16
10010100 => 00101001 => 16
10010101 => 10101001 => 17
10010110 => 01101001 => 18
10010111 => 11101001 => 19
10011000 => 00011001 => 17
10011001 => 10011001 => 18
10011010 => 01011001 => 19
10011011 => 11011001 => 20
10011100 => 00111001 => 20
10011101 => 10111001 => 21
10011110 => 01111001 => 22
10011111 => 11111001 => 23
10100000 => 00000101 => 14
10100001 => 10000101 => 15
10100010 => 01000101 => 16
10100011 => 11000101 => 17
10100100 => 00100101 => 17
10100101 => 10100101 => 18
10100110 => 01100101 => 19
10100111 => 11100101 => 20
10101000 => 00010101 => 18
10101001 => 10010101 => 19
10101010 => 01010101 => 20
10101011 => 11010101 => 21
10101100 => 00110101 => 21
10101101 => 10110101 => 22
10101110 => 01110101 => 23
10101111 => 11110101 => 24
10110000 => 00001101 => 19
10110001 => 10001101 => 20
10110010 => 01001101 => 21
10110011 => 11001101 => 22
10110100 => 00101101 => 22
10110101 => 10101101 => 23
10110110 => 01101101 => 24
10110111 => 11101101 => 25
10111000 => 00011101 => 23
10111001 => 10011101 => 24
10111010 => 01011101 => 25
10111011 => 11011101 => 26
10111100 => 00111101 => 26
10111101 => 10111101 => 27
10111110 => 01111101 => 28
10111111 => 11111101 => 29
11000000 => 00000011 => 15
11000001 => 10000011 => 16
11000010 => 01000011 => 17
11000011 => 11000011 => 18
11000100 => 00100011 => 18
11000101 => 10100011 => 19
11000110 => 01100011 => 20
11000111 => 11100011 => 21
11001000 => 00010011 => 19
11001001 => 10010011 => 20
11001010 => 01010011 => 21
11001011 => 11010011 => 22
11001100 => 00110011 => 22
11001101 => 10110011 => 23
11001110 => 01110011 => 24
11001111 => 11110011 => 25
11010000 => 00001011 => 20
11010001 => 10001011 => 21
11010010 => 01001011 => 22
11010011 => 11001011 => 23
11010100 => 00101011 => 23
11010101 => 10101011 => 24
11010110 => 01101011 => 25
11010111 => 11101011 => 26
11011000 => 00011011 => 24
11011001 => 10011011 => 25
11011010 => 01011011 => 26
11011011 => 11011011 => 27
11011100 => 00111011 => 27
11011101 => 10111011 => 28
11011110 => 01111011 => 29
11011111 => 11111011 => 30
11100000 => 00000111 => 21
11100001 => 10000111 => 22
11100010 => 01000111 => 23
11100011 => 11000111 => 24
11100100 => 00100111 => 24
11100101 => 10100111 => 25
11100110 => 01100111 => 26
11100111 => 11100111 => 27
11101000 => 00010111 => 25
11101001 => 10010111 => 26
11101010 => 01010111 => 27
11101011 => 11010111 => 28
11101100 => 00110111 => 28
11101101 => 10110111 => 29
11101110 => 01110111 => 30
11101111 => 11110111 => 31
11110000 => 00001111 => 26
11110001 => 10001111 => 27
11110010 => 01001111 => 28
11110011 => 11001111 => 29
11110100 => 00101111 => 29
11110101 => 10101111 => 30
11110110 => 01101111 => 31
11110111 => 11101111 => 32
11111000 => 00011111 => 30
11111001 => 10011111 => 31
11111010 => 01011111 => 32
11111011 => 11011111 => 33
11111100 => 00111111 => 33
11111101 => 10111111 => 34
11111110 => 01111111 => 35
11111111 => 11111111 => 36
000000000 => 000000000 => 0
000000001 => 100000000 => 1
000000010 => 010000000 => 2
000000011 => 110000000 => 3
000000100 => 001000000 => 3
000000101 => 101000000 => 4
000000110 => 011000000 => 5
000000111 => 111000000 => 6
000001000 => 000100000 => 4
000001001 => 100100000 => 5
000001010 => 010100000 => 6
000001011 => 110100000 => 7
000001100 => 001100000 => 7
000001101 => 101100000 => 8
000001110 => 011100000 => 9
000001111 => 111100000 => 10
000010000 => 000010000 => 5
000010001 => 100010000 => 6
000010010 => 010010000 => 7
000010011 => 110010000 => 8
000010100 => 001010000 => 8
000010101 => 101010000 => 9
000010110 => 011010000 => 10
000010111 => 111010000 => 11
000011000 => 000110000 => 9
000011001 => 100110000 => 10
000011010 => 010110000 => 11
000011011 => 110110000 => 12
000011100 => 001110000 => 12
000011101 => 101110000 => 13
000011110 => 011110000 => 14
000011111 => 111110000 => 15
000100000 => 000001000 => 6
000100001 => 100001000 => 7
000100010 => 010001000 => 8
000100011 => 110001000 => 9
000100100 => 001001000 => 9
000100101 => 101001000 => 10
000100110 => 011001000 => 11
000100111 => 111001000 => 12
000101000 => 000101000 => 10
000101001 => 100101000 => 11
000101010 => 010101000 => 12
000101011 => 110101000 => 13
000101100 => 001101000 => 13
000101101 => 101101000 => 14
000101110 => 011101000 => 15
000101111 => 111101000 => 16
000110000 => 000011000 => 11
000110001 => 100011000 => 12
000110010 => 010011000 => 13
000110011 => 110011000 => 14
000110100 => 001011000 => 14
000110101 => 101011000 => 15
000110110 => 011011000 => 16
000110111 => 111011000 => 17
000111000 => 000111000 => 15
000111001 => 100111000 => 16
000111010 => 010111000 => 17
000111011 => 110111000 => 18
000111100 => 001111000 => 18
000111101 => 101111000 => 19
000111110 => 011111000 => 20
000111111 => 111111000 => 21
001000000 => 000000100 => 7
001000001 => 100000100 => 8
001000010 => 010000100 => 9
001000011 => 110000100 => 10
001000100 => 001000100 => 10
001000101 => 101000100 => 11
001000110 => 011000100 => 12
001000111 => 111000100 => 13
001001000 => 000100100 => 11
001001001 => 100100100 => 12
001001010 => 010100100 => 13
001001011 => 110100100 => 14
001001100 => 001100100 => 14
001001101 => 101100100 => 15
001001110 => 011100100 => 16
001001111 => 111100100 => 17
001010000 => 000010100 => 12
001010001 => 100010100 => 13
001010010 => 010010100 => 14
001010011 => 110010100 => 15
001010100 => 001010100 => 15
001010101 => 101010100 => 16
001010110 => 011010100 => 17
001010111 => 111010100 => 18
001011000 => 000110100 => 16
001011001 => 100110100 => 17
001011010 => 010110100 => 18
001011011 => 110110100 => 19
001011100 => 001110100 => 19
001011101 => 101110100 => 20
001011110 => 011110100 => 21
001011111 => 111110100 => 22
001100000 => 000001100 => 13
001100001 => 100001100 => 14
001100010 => 010001100 => 15
001100011 => 110001100 => 16
001100100 => 001001100 => 16
001100101 => 101001100 => 17
001100110 => 011001100 => 18
001100111 => 111001100 => 19
001101000 => 000101100 => 17
001101001 => 100101100 => 18
001101010 => 010101100 => 19
001101011 => 110101100 => 20
001101100 => 001101100 => 20
001101101 => 101101100 => 21
001101110 => 011101100 => 22
001101111 => 111101100 => 23
001110000 => 000011100 => 18
001110001 => 100011100 => 19
001110010 => 010011100 => 20
001110011 => 110011100 => 21
001110100 => 001011100 => 21
001110101 => 101011100 => 22
001110110 => 011011100 => 23
001110111 => 111011100 => 24
001111000 => 000111100 => 22
001111001 => 100111100 => 23
001111010 => 010111100 => 24
001111011 => 110111100 => 25
001111100 => 001111100 => 25
001111101 => 101111100 => 26
001111110 => 011111100 => 27
001111111 => 111111100 => 28
010000000 => 000000010 => 8
010000001 => 100000010 => 9
010000010 => 010000010 => 10
010000011 => 110000010 => 11
010000100 => 001000010 => 11
010000101 => 101000010 => 12
010000110 => 011000010 => 13
010000111 => 111000010 => 14
010001000 => 000100010 => 12
010001001 => 100100010 => 13
010001010 => 010100010 => 14
010001011 => 110100010 => 15
010001100 => 001100010 => 15
010001101 => 101100010 => 16
010001110 => 011100010 => 17
010001111 => 111100010 => 18
010010000 => 000010010 => 13
010010001 => 100010010 => 14
010010010 => 010010010 => 15
010010011 => 110010010 => 16
010010100 => 001010010 => 16
010010101 => 101010010 => 17
010010110 => 011010010 => 18
010010111 => 111010010 => 19
010011000 => 000110010 => 17
010011001 => 100110010 => 18
010011010 => 010110010 => 19
010011011 => 110110010 => 20
010011100 => 001110010 => 20
010011101 => 101110010 => 21
010011110 => 011110010 => 22
010011111 => 111110010 => 23
010100000 => 000001010 => 14
010100001 => 100001010 => 15
010100010 => 010001010 => 16
010100011 => 110001010 => 17
010100100 => 001001010 => 17
010100101 => 101001010 => 18
010100110 => 011001010 => 19
010100111 => 111001010 => 20
010101000 => 000101010 => 18
010101001 => 100101010 => 19
010101010 => 010101010 => 20
010101011 => 110101010 => 21
010101100 => 001101010 => 21
010101101 => 101101010 => 22
010101110 => 011101010 => 23
010101111 => 111101010 => 24
010110000 => 000011010 => 19
010110001 => 100011010 => 20
010110010 => 010011010 => 21
010110011 => 110011010 => 22
010110100 => 001011010 => 22
010110101 => 101011010 => 23
010110110 => 011011010 => 24
010110111 => 111011010 => 25
010111000 => 000111010 => 23
010111001 => 100111010 => 24
010111010 => 010111010 => 25
010111011 => 110111010 => 26
010111100 => 001111010 => 26
010111101 => 101111010 => 27
010111110 => 011111010 => 28
010111111 => 111111010 => 29
011000000 => 000000110 => 15
011000001 => 100000110 => 16
011000010 => 010000110 => 17
011000011 => 110000110 => 18
011000100 => 001000110 => 18
011000101 => 101000110 => 19
011000110 => 011000110 => 20
011000111 => 111000110 => 21
011001000 => 000100110 => 19
011001001 => 100100110 => 20
011001010 => 010100110 => 21
011001011 => 110100110 => 22
011001100 => 001100110 => 22
011001101 => 101100110 => 23
011001110 => 011100110 => 24
011001111 => 111100110 => 25
011010000 => 000010110 => 20
011010001 => 100010110 => 21
011010010 => 010010110 => 22
011010011 => 110010110 => 23
011010100 => 001010110 => 23
011010101 => 101010110 => 24
011010110 => 011010110 => 25
011010111 => 111010110 => 26
011011000 => 000110110 => 24
011011001 => 100110110 => 25
011011010 => 010110110 => 26
011011011 => 110110110 => 27
011011100 => 001110110 => 27
011011101 => 101110110 => 28
011011110 => 011110110 => 29
011011111 => 111110110 => 30
011100000 => 000001110 => 21
011100001 => 100001110 => 22
011100010 => 010001110 => 23
011100011 => 110001110 => 24
011100100 => 001001110 => 24
011100101 => 101001110 => 25
011100110 => 011001110 => 26
011100111 => 111001110 => 27
011101000 => 000101110 => 25
011101001 => 100101110 => 26
011101010 => 010101110 => 27
011101011 => 110101110 => 28
011101100 => 001101110 => 28
011101101 => 101101110 => 29
011101110 => 011101110 => 30
011101111 => 111101110 => 31
011110000 => 000011110 => 26
011110001 => 100011110 => 27
011110010 => 010011110 => 28
011110011 => 110011110 => 29
011110100 => 001011110 => 29
011110101 => 101011110 => 30
011110110 => 011011110 => 31
011110111 => 111011110 => 32
011111000 => 000111110 => 30
011111001 => 100111110 => 31
011111010 => 010111110 => 32
011111011 => 110111110 => 33
011111100 => 001111110 => 33
011111101 => 101111110 => 34
011111110 => 011111110 => 35
011111111 => 111111110 => 36
100000000 => 000000001 => 9
100000001 => 100000001 => 10
100000010 => 010000001 => 11
100000011 => 110000001 => 12
100000100 => 001000001 => 12
100000101 => 101000001 => 13
100000110 => 011000001 => 14
100000111 => 111000001 => 15
100001000 => 000100001 => 13
100001001 => 100100001 => 14
100001010 => 010100001 => 15
100001011 => 110100001 => 16
100001100 => 001100001 => 16
100001101 => 101100001 => 17
100001110 => 011100001 => 18
100001111 => 111100001 => 19
100010000 => 000010001 => 14
100010001 => 100010001 => 15
100010010 => 010010001 => 16
100010011 => 110010001 => 17
100010100 => 001010001 => 17
100010101 => 101010001 => 18
100010110 => 011010001 => 19
100010111 => 111010001 => 20
100011000 => 000110001 => 18
100011001 => 100110001 => 19
100011010 => 010110001 => 20
100011011 => 110110001 => 21
100011100 => 001110001 => 21
100011101 => 101110001 => 22
100011110 => 011110001 => 23
100011111 => 111110001 => 24
100100000 => 000001001 => 15
100100001 => 100001001 => 16
100100010 => 010001001 => 17
100100011 => 110001001 => 18
100100100 => 001001001 => 18
100100101 => 101001001 => 19
100100110 => 011001001 => 20
100100111 => 111001001 => 21
100101000 => 000101001 => 19
100101001 => 100101001 => 20
100101010 => 010101001 => 21
100101011 => 110101001 => 22
100101100 => 001101001 => 22
100101101 => 101101001 => 23
100101110 => 011101001 => 24
100101111 => 111101001 => 25
100110000 => 000011001 => 20
100110001 => 100011001 => 21
100110010 => 010011001 => 22
100110011 => 110011001 => 23
100110100 => 001011001 => 23
100110101 => 101011001 => 24
100110110 => 011011001 => 25
100110111 => 111011001 => 26
100111000 => 000111001 => 24
100111001 => 100111001 => 25
100111010 => 010111001 => 26
100111011 => 110111001 => 27
100111100 => 001111001 => 27
100111101 => 101111001 => 28
100111110 => 011111001 => 29
100111111 => 111111001 => 30
101000000 => 000000101 => 16
101000001 => 100000101 => 17
101000010 => 010000101 => 18
101000011 => 110000101 => 19
101000100 => 001000101 => 19
101000101 => 101000101 => 20
101000110 => 011000101 => 21
101000111 => 111000101 => 22
101001000 => 000100101 => 20
101001001 => 100100101 => 21
101001010 => 010100101 => 22
101001011 => 110100101 => 23
101001100 => 001100101 => 23
101001101 => 101100101 => 24
101001110 => 011100101 => 25
101001111 => 111100101 => 26
101010000 => 000010101 => 21
101010001 => 100010101 => 22
101010010 => 010010101 => 23
101010011 => 110010101 => 24
101010100 => 001010101 => 24
101010101 => 101010101 => 25
101010110 => 011010101 => 26
101010111 => 111010101 => 27
101011000 => 000110101 => 25
101011001 => 100110101 => 26
101011010 => 010110101 => 27
101011011 => 110110101 => 28
101011100 => 001110101 => 28
101011101 => 101110101 => 29
101011110 => 011110101 => 30
101011111 => 111110101 => 31
101100000 => 000001101 => 22
101100001 => 100001101 => 23
101100010 => 010001101 => 24
101100011 => 110001101 => 25
101100100 => 001001101 => 25
101100101 => 101001101 => 26
101100110 => 011001101 => 27
101100111 => 111001101 => 28
101101000 => 000101101 => 26
101101001 => 100101101 => 27
101101010 => 010101101 => 28
101101011 => 110101101 => 29
101101100 => 001101101 => 29
101101101 => 101101101 => 30
101101110 => 011101101 => 31
101101111 => 111101101 => 32
101110000 => 000011101 => 27
101110001 => 100011101 => 28
101110010 => 010011101 => 29
101110011 => 110011101 => 30
101110100 => 001011101 => 30
101110101 => 101011101 => 31
101110110 => 011011101 => 32
101110111 => 111011101 => 33
101111000 => 000111101 => 31
101111001 => 100111101 => 32
101111010 => 010111101 => 33
101111011 => 110111101 => 34
101111100 => 001111101 => 34
101111101 => 101111101 => 35
101111110 => 011111101 => 36
101111111 => 111111101 => 37
110000000 => 000000011 => 17
110000001 => 100000011 => 18
110000010 => 010000011 => 19
110000011 => 110000011 => 20
110000100 => 001000011 => 20
110000101 => 101000011 => 21
110000110 => 011000011 => 22
110000111 => 111000011 => 23
110001000 => 000100011 => 21
110001001 => 100100011 => 22
110001010 => 010100011 => 23
110001011 => 110100011 => 24
110001100 => 001100011 => 24
110001101 => 101100011 => 25
110001110 => 011100011 => 26
110001111 => 111100011 => 27
110010000 => 000010011 => 22
110010001 => 100010011 => 23
110010010 => 010010011 => 24
110010011 => 110010011 => 25
110010100 => 001010011 => 25
110010101 => 101010011 => 26
110010110 => 011010011 => 27
110010111 => 111010011 => 28
110011000 => 000110011 => 26
110011001 => 100110011 => 27
110011010 => 010110011 => 28
110011011 => 110110011 => 29
110011100 => 001110011 => 29
110011101 => 101110011 => 30
110011110 => 011110011 => 31
110011111 => 111110011 => 32
110100000 => 000001011 => 23
110100001 => 100001011 => 24
110100010 => 010001011 => 25
110100011 => 110001011 => 26
110100100 => 001001011 => 26
110100101 => 101001011 => 27
110100110 => 011001011 => 28
110100111 => 111001011 => 29
110101000 => 000101011 => 27
110101001 => 100101011 => 28
110101010 => 010101011 => 29
110101011 => 110101011 => 30
110101100 => 001101011 => 30
110101101 => 101101011 => 31
110101110 => 011101011 => 32
110101111 => 111101011 => 33
110110000 => 000011011 => 28
110110001 => 100011011 => 29
110110010 => 010011011 => 30
110110011 => 110011011 => 31
110110100 => 001011011 => 31
110110101 => 101011011 => 32
110110110 => 011011011 => 33
110110111 => 111011011 => 34
110111000 => 000111011 => 32
110111001 => 100111011 => 33
110111010 => 010111011 => 34
110111011 => 110111011 => 35
110111100 => 001111011 => 35
110111101 => 101111011 => 36
110111110 => 011111011 => 37
110111111 => 111111011 => 38
111000000 => 000000111 => 24
111000001 => 100000111 => 25
111000010 => 010000111 => 26
111000011 => 110000111 => 27
111000100 => 001000111 => 27
111000101 => 101000111 => 28
111000110 => 011000111 => 29
111000111 => 111000111 => 30
111001000 => 000100111 => 28
111001001 => 100100111 => 29
111001010 => 010100111 => 30
111001011 => 110100111 => 31
111001100 => 001100111 => 31
111001101 => 101100111 => 32
111001110 => 011100111 => 33
111001111 => 111100111 => 34
111010000 => 000010111 => 29
111010001 => 100010111 => 30
111010010 => 010010111 => 31
111010011 => 110010111 => 32
111010100 => 001010111 => 32
111010101 => 101010111 => 33
111010110 => 011010111 => 34
111010111 => 111010111 => 35
111011000 => 000110111 => 33
111011001 => 100110111 => 34
111011010 => 010110111 => 35
111011011 => 110110111 => 36
111011100 => 001110111 => 36
111011101 => 101110111 => 37
111011110 => 011110111 => 38
111011111 => 111110111 => 39
111100000 => 000001111 => 30
111100001 => 100001111 => 31
111100010 => 010001111 => 32
111100011 => 110001111 => 33
111100100 => 001001111 => 33
111100101 => 101001111 => 34
111100110 => 011001111 => 35
111100111 => 111001111 => 36
111101000 => 000101111 => 34
111101001 => 100101111 => 35
111101010 => 010101111 => 36
111101011 => 110101111 => 37
111101100 => 001101111 => 37
111101101 => 101101111 => 38
111101110 => 011101111 => 39
111101111 => 111101111 => 40
111110000 => 000011111 => 35
111110001 => 100011111 => 36
111110010 => 010011111 => 37
111110011 => 110011111 => 38
111110100 => 001011111 => 38
111110101 => 101011111 => 39
111110110 => 011011111 => 40
111110111 => 111011111 => 41
111111000 => 000111111 => 39
111111001 => 100111111 => 40
111111010 => 010111111 => 41
111111011 => 110111111 => 42
111111100 => 001111111 => 42
111111101 => 101111111 => 43
111111110 => 011111111 => 44
111111111 => 111111111 => 45
1010111000 => 0001110101 => 33
1011010100 => 0010101101 => 33
1011011000 => 0001101101 => 34
1011100100 => 0010011101 => 34
1011101000 => 0001011101 => 35
1011110000 => 0000111101 => 36
1100111000 => 0001110011 => 34
1101010100 => 0010101011 => 34
1101011000 => 0001101011 => 35
1101100100 => 0010011011 => 35
1101101000 => 0001011011 => 36
1101110000 => 0000111011 => 37
1110010100 => 0010100111 => 35
1110011000 => 0001100111 => 36
1110100100 => 0010010111 => 36
1110101000 => 0001010111 => 37
1110110000 => 0000110111 => 38
1111000100 => 0010001111 => 37
1111001000 => 0001001111 => 38
1111010000 => 0000101111 => 39
1111100000 => 0000011111 => 40
1111111000 => 0001111111 => 49
1111110000 => 0000111111 => 45
1111101000 => 0001011111 => 44
1111100100 => 0010011111 => 43
1111011000 => 0001101111 => 43
1111010100 => 0010101111 => 42
1111000000 => 0000001111 => 34
1110111000 => 0001110111 => 42
1110100000 => 0000010111 => 33
1110010000 => 0000100111 => 32
1110001000 => 0001000111 => 31
1110000100 => 0010000111 => 30
1110000000 => 0000000111 => 27
1101111000 => 0001111011 => 41
1101100000 => 0000011011 => 32
1101010000 => 0000101011 => 31
1101001000 => 0001001011 => 30
1101000100 => 0010001011 => 29
1101000000 => 0000001011 => 26
1100110000 => 0000110011 => 30
1100101000 => 0001010011 => 29
1100100100 => 0010010011 => 28
1100100000 => 0000010011 => 25
1100011000 => 0001100011 => 28
1100010100 => 0010100011 => 27
1100010000 => 0000100011 => 24
1100001000 => 0001000011 => 23
1100000100 => 0010000011 => 22
1100000000 => 0000000011 => 19
1011111000 => 0001111101 => 40
1011100000 => 0000011101 => 31
1011010000 => 0000101101 => 30
1011001000 => 0001001101 => 29
1011000100 => 0010001101 => 28
1011000000 => 0000001101 => 25
1010110000 => 0000110101 => 29
1010101000 => 0001010101 => 28
1010100100 => 0010010101 => 27
1010100000 => 0000010101 => 24
1010011000 => 0001100101 => 27
1010010100 => 0010100101 => 26
1010010000 => 0000100101 => 23
1010001000 => 0001000101 => 22
1010000100 => 0010000101 => 21
1010000000 => 0000000101 => 18
1001111000 => 0001111001 => 32
1001110000 => 0000111001 => 28
1001101000 => 0001011001 => 27
1001100100 => 0010011001 => 26
1001100000 => 0000011001 => 23
1001011000 => 0001101001 => 26
1001010100 => 0010101001 => 25
1001010000 => 0000101001 => 22
1001001000 => 0001001001 => 21
1001000100 => 0010001001 => 20
1001000000 => 0000001001 => 17
1000111000 => 0001110001 => 25
1000110100 => 0010110001 => 24
1000110000 => 0000110001 => 21
1000101000 => 0001010001 => 20
1000100100 => 0010010001 => 19
1000100000 => 0000010001 => 16
1000011000 => 0001100001 => 19
1000010100 => 0010100001 => 18
1000010000 => 0000100001 => 15
1000001000 => 0001000001 => 14
1000000100 => 0010000001 => 13
1000000000 => 0000000001 => 10
0000000000 => 0000000000 => 0
0000011000 => 0001100000 => 9
0001100000 => 0000011000 => 13
0001111000 => 0001111000 => 22
0001001000 => 0001001000 => 11
0110000000 => 0000000110 => 17
0110011000 => 0001100110 => 26
0111100000 => 0000011110 => 30
0111111000 => 0001111110 => 39
0111001000 => 0001001110 => 28
0100100000 => 0000010010 => 15
0100111000 => 0001110010 => 24
0100001000 => 0001000010 => 13
0101101000 => 0001011010 => 26
0010101000 => 0001010100 => 18
0010100100 => 0010010100 => 17
0010010100 => 0010100100 => 16
0011010100 => 0010101100 => 23
0001010100 => 0010101000 => 15
0101010100 => 0010101010 => 24
0010100000 => 0000010100 => 14
0010000100 => 0010000100 => 11
0000010100 => 0010100000 => 8
0111010100 => 0010101110 => 32
0000000100 => 0010000000 => 3
0010111000 => 0001110100 => 23
0011011000 => 0001101100 => 24
0011100100 => 0010011100 => 24
0011101000 => 0001011100 => 25
0011110000 => 0000111100 => 26
0101011000 => 0001101010 => 25
0101100100 => 0010011010 => 25
0101110000 => 0000111010 => 27
0110010100 => 0010100110 => 25
0110100100 => 0010010110 => 26
0110101000 => 0001010110 => 27
0110110000 => 0000110110 => 28
0111000100 => 0010001110 => 27
0111010000 => 0000101110 => 29
0100000000 => 0000000010 => 9
0101111000 => 0001111010 => 31
0110111000 => 0001110110 => 32
0111011000 => 0001101110 => 33
0111100100 => 0010011110 => 33
0111101000 => 0001011110 => 34
0111110000 => 0000111110 => 35
0100000100 => 0010000010 => 12
0011111000 => 0001111100 => 30
0000110100 => 0010110000 => 14
0101000000 => 0000001010 => 16
0001010000 => 0000101000 => 12
0100010000 => 0000100010 => 14
0001000100 => 0010001000 => 10
0111000000 => 0000001110 => 24
0010000000 => 0000000100 => 8
0110100000 => 0000010110 => 23
0000100100 => 0010010000 => 9
0011000000 => 0000001100 => 15
0010110000 => 0000110100 => 19
0000001000 => 0001000000 => 4
0000101000 => 0001010000 => 10
0010001000 => 0001000100 => 12
0011000100 => 0010001100 => 18
0001100100 => 0010011000 => 16
0101001000 => 0001001010 => 20
0101010000 => 0000101010 => 21
0010010000 => 0000100100 => 13
0100101000 => 0001010010 => 19
0001000000 => 0000001000 => 7
0100011000 => 0001100010 => 18
0010011000 => 0001100100 => 17
0001011000 => 0001101000 => 16
0000100000 => 0000010000 => 6
0000110000 => 0000110000 => 11
0101100000 => 0000011010 => 22
0000111000 => 0001110000 => 15
0000010000 => 0000100000 => 5
0011100000 => 0000011100 => 21
0101000100 => 0010001010 => 19
0100010100 => 0010100010 => 17
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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 1,1,1,1 1,1,1,2,1,1,1 1,1,1,2,2,2,2,2,1,1,1 1,1,1,2,2,3,3,3,3,3,3,2,2,1,1,1 1,1,1,2,2,3,4,4,4,5,5,5,5,4,4,4,3,2,2,1,1,1 1,1,1,2,2,3,4,5,5,6,7,7,8,8,8,8,8,7,7,6,5,5,4,3,2,2,1,1,1
$F_{1} = 1 + q$
$F_{2} = 1 + q + q^{2} + q^{3}$
$F_{3} = 1 + q + q^{2} + 2\ q^{3} + q^{4} + q^{5} + q^{6}$
$F_{4} = 1 + q + q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{6} + 2\ q^{7} + q^{8} + q^{9} + q^{10}$
$F_{5} = 1 + q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 3\ q^{6} + 3\ q^{7} + 3\ q^{8} + 3\ q^{9} + 3\ q^{10} + 2\ q^{11} + 2\ q^{12} + q^{13} + q^{14} + q^{15}$
$F_{6} = 1 + q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 4\ q^{6} + 4\ q^{7} + 4\ q^{8} + 5\ q^{9} + 5\ q^{10} + 5\ q^{11} + 5\ q^{12} + 4\ q^{13} + 4\ q^{14} + 4\ q^{15} + 3\ q^{16} + 2\ q^{17} + 2\ q^{18} + q^{19} + q^{20} + q^{21}$
$F_{7} = 1 + q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 4\ q^{6} + 5\ q^{7} + 5\ q^{8} + 6\ q^{9} + 7\ q^{10} + 7\ q^{11} + 8\ q^{12} + 8\ q^{13} + 8\ q^{14} + 8\ q^{15} + 8\ q^{16} + 7\ q^{17} + 7\ q^{18} + 6\ q^{19} + 5\ q^{20} + 5\ q^{21} + 4\ q^{22} + 3\ q^{23} + 2\ q^{24} + 2\ q^{25} + q^{26} + q^{27} + q^{28}$
$F_{8} = 1 + q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 4\ q^{6} + 5\ q^{7} + 6\ q^{8} + 7\ q^{9} + 8\ q^{10} + 9\ q^{11} + 10\ q^{12} + 11\ q^{13} + 12\ q^{14} + 13\ q^{15} + 13\ q^{16} + 13\ q^{17} + 14\ q^{18} + 13\ q^{19} + 13\ q^{20} + 13\ q^{21} + 12\ q^{22} + 11\ q^{23} + 10\ q^{24} + 9\ q^{25} + 8\ q^{26} + 7\ q^{27} + 6\ q^{28} + 5\ q^{29} + 4\ q^{30} + 3\ q^{31} + 2\ q^{32} + 2\ q^{33} + q^{34} + q^{35} + q^{36}$
$F_{9} = 1 + q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 4\ q^{6} + 5\ q^{7} + 6\ q^{8} + 8\ q^{9} + 9\ q^{10} + 10\ q^{11} + 12\ q^{12} + 13\ q^{13} + 15\ q^{14} + 17\ q^{15} + 18\ q^{16} + 19\ q^{17} + 21\ q^{18} + 21\ q^{19} + 22\ q^{20} + 23\ q^{21} + 23\ q^{22} + 23\ q^{23} + 23\ q^{24} + 22\ q^{25} + 21\ q^{26} + 21\ q^{27} + 19\ q^{28} + 18\ q^{29} + 17\ q^{30} + 15\ q^{31} + 13\ q^{32} + 12\ q^{33} + 10\ q^{34} + 9\ q^{35} + 8\ q^{36} + 6\ q^{37} + 5\ q^{38} + 4\ q^{39} + 3\ q^{40} + 2\ q^{41} + 2\ q^{42} + q^{43} + q^{44} + q^{45}$
Description
The sum of the positions of the ones in a binary word.
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