Identifier
Identifier
Values
0 => 2
1 => 2
00 => 3
01 => 4
10 => 4
11 => 3
000 => 4
001 => 6
010 => 6
011 => 6
100 => 6
101 => 6
110 => 6
111 => 4
0000 => 5
0001 => 8
0010 => 9
0011 => 9
0100 => 9
0101 => 8
0110 => 9
0111 => 8
1000 => 8
1001 => 9
1010 => 8
1011 => 9
1100 => 9
1101 => 9
1110 => 8
1111 => 5
00000 => 6
00001 => 10
00010 => 12
00011 => 12
00100 => 12
00101 => 12
00110 => 13
00111 => 12
01000 => 12
01001 => 12
01010 => 10
01011 => 12
01100 => 13
01101 => 12
01110 => 12
01111 => 10
10000 => 10
10001 => 12
10010 => 12
10011 => 13
10100 => 12
10101 => 10
10110 => 12
10111 => 12
11000 => 12
11001 => 13
11010 => 12
11011 => 12
11100 => 12
11101 => 12
11110 => 10
11111 => 6
000000 => 7
000001 => 12
000010 => 15
000011 => 15
000100 => 16
000101 => 16
000110 => 17
000111 => 16
001000 => 16
001001 => 15
001010 => 15
001011 => 17
001100 => 17
001101 => 17
001110 => 17
001111 => 15
010000 => 15
010001 => 16
010010 => 15
010011 => 17
010100 => 15
010101 => 12
010110 => 16
010111 => 16
011000 => 17
011001 => 17
011010 => 16
011011 => 15
011100 => 17
011101 => 16
011110 => 15
011111 => 12
100000 => 12
100001 => 15
100010 => 16
100011 => 17
100100 => 15
100101 => 16
100110 => 17
100111 => 17
101000 => 16
101001 => 16
101010 => 12
101011 => 15
101100 => 17
101101 => 15
101110 => 16
101111 => 15
110000 => 15
110001 => 17
110010 => 17
110011 => 17
110100 => 17
110101 => 15
110110 => 15
110111 => 16
111000 => 16
111001 => 17
111010 => 16
111011 => 16
111100 => 15
111101 => 15
111110 => 12
111111 => 7
0000000 => 8
0000001 => 14
0000010 => 18
0000011 => 18
0000100 => 20
0000101 => 20
0000110 => 21
0000111 => 20
0001000 => 20
0001001 => 20
0001010 => 20
0001011 => 22
0001100 => 22
0001101 => 22
0001110 => 22
0001111 => 20
0010000 => 20
0010001 => 20
0010010 => 18
0010011 => 21
0010100 => 20
0010101 => 18
0010110 => 22
0010111 => 22
0011000 => 22
0011001 => 21
0011010 => 22
0011011 => 21
0011100 => 22
0011101 => 22
0011110 => 21
0011111 => 18
0100000 => 18
0100001 => 20
0100010 => 20
0100011 => 22
0100100 => 18
0100101 => 20
0100110 => 22
0100111 => 22
0101000 => 20
0101001 => 20
0101010 => 14
0101011 => 18
0101100 => 22
0101101 => 20
0101110 => 21
0101111 => 20
0110000 => 21
0110001 => 22
0110010 => 22
0110011 => 21
0110100 => 22
0110101 => 20
0110110 => 18
0110111 => 20
0111000 => 22
0111001 => 22
0111010 => 21
0111011 => 20
0111100 => 21
0111101 => 20
0111110 => 18
0111111 => 14
1000000 => 14
1000001 => 18
1000010 => 20
1000011 => 21
1000100 => 20
1000101 => 21
1000110 => 22
1000111 => 22
1001000 => 20
1001001 => 18
1001010 => 20
1001011 => 22
1001100 => 21
1001101 => 22
1001110 => 22
1001111 => 21
1010000 => 20
1010001 => 21
1010010 => 20
1010011 => 22
1010100 => 18
1010101 => 14
1010110 => 20
1010111 => 20
1011000 => 22
1011001 => 22
1011010 => 20
1011011 => 18
1011100 => 22
1011101 => 20
1011110 => 20
1011111 => 18
1100000 => 18
1100001 => 21
1100010 => 22
1100011 => 22
1100100 => 21
1100101 => 22
1100110 => 21
1100111 => 22
1101000 => 22
1101001 => 22
1101010 => 18
1101011 => 20
1101100 => 21
1101101 => 18
1101110 => 20
1101111 => 20
1110000 => 20
1110001 => 22
1110010 => 22
1110011 => 22
1110100 => 22
1110101 => 20
1110110 => 20
1110111 => 20
1111000 => 20
1111001 => 21
1111010 => 20
1111011 => 20
1111100 => 18
1111101 => 18
1111110 => 14
1111111 => 8
00000000 => 9
00000001 => 16
00000010 => 21
00000011 => 21
00000100 => 24
00000101 => 24
00000110 => 25
00000111 => 24
00001000 => 25
00001001 => 25
00001010 => 25
00001011 => 27
00001100 => 27
00001101 => 27
00001110 => 27
00001111 => 25
00010000 => 25
00010001 => 24
00010010 => 24
00010011 => 27
00010100 => 26
00010101 => 24
00010110 => 28
00010111 => 28
00011000 => 27
00011001 => 27
00011010 => 28
00011011 => 27
00011100 => 28
00011101 => 28
00011110 => 27
00011111 => 24
00100000 => 24
00100001 => 25
00100010 => 24
00100011 => 27
00100100 => 21
00100101 => 24
00100110 => 27
00100111 => 27
00101000 => 26
00101001 => 25
00101010 => 21
00101011 => 25
00101100 => 28
00101101 => 27
00101110 => 28
00101111 => 27
00110000 => 27
00110001 => 27
00110010 => 27
00110011 => 25
00110100 => 28
00110101 => 27
00110110 => 25
00110111 => 27
00111000 => 28
00111001 => 27
00111010 => 28
00111011 => 27
00111100 => 27
00111101 => 27
00111110 => 25
00111111 => 21
01000000 => 21
01000001 => 24
01000010 => 25
01000011 => 27
01000100 => 24
01000101 => 26
01000110 => 28
01000111 => 28
01001000 => 24
01001001 => 21
01001010 => 25
01001011 => 27
01001100 => 27
01001101 => 28
01001110 => 28
01001111 => 27
01010000 => 25
01010001 => 26
01010010 => 25
01010011 => 27
01010100 => 21
01010101 => 16
01010110 => 24
01010111 => 24
01011000 => 28
01011001 => 28
01011010 => 25
01011011 => 24
01011100 => 28
01011101 => 26
01011110 => 26
01011111 => 24
01100000 => 25
01100001 => 27
01100010 => 28
01100011 => 27
01100100 => 27
01100101 => 28
01100110 => 25
01100111 => 27
01101000 => 28
01101001 => 28
01101010 => 24
01101011 => 25
01101100 => 25
01101101 => 21
01101110 => 25
01101111 => 25
01110000 => 27
01110001 => 28
01110010 => 28
01110011 => 27
01110100 => 28
01110101 => 26
01110110 => 25
01110111 => 24
01111000 => 27
01111001 => 27
01111010 => 26
01111011 => 25
01111100 => 25
01111101 => 24
01111110 => 21
01111111 => 16
10000000 => 16
10000001 => 21
10000010 => 24
10000011 => 25
10000100 => 25
10000101 => 26
10000110 => 27
10000111 => 27
10001000 => 24
10001001 => 25
10001010 => 26
10001011 => 28
10001100 => 27
10001101 => 28
10001110 => 28
10001111 => 27
10010000 => 25
10010001 => 25
10010010 => 21
10010011 => 25
10010100 => 25
10010101 => 24
10010110 => 28
10010111 => 28
10011000 => 27
10011001 => 25
10011010 => 28
10011011 => 27
10011100 => 27
10011101 => 28
10011110 => 27
10011111 => 25
10100000 => 24
10100001 => 26
10100010 => 26
10100011 => 28
10100100 => 24
10100101 => 25
10100110 => 28
10100111 => 28
10101000 => 24
10101001 => 24
10101010 => 16
10101011 => 21
10101100 => 27
10101101 => 25
10101110 => 26
10101111 => 25
10110000 => 27
10110001 => 28
10110010 => 28
10110011 => 27
10110100 => 27
10110101 => 25
10110110 => 21
10110111 => 24
10111000 => 28
10111001 => 28
10111010 => 26
10111011 => 24
10111100 => 27
10111101 => 25
10111110 => 24
10111111 => 21
11000000 => 21
11000001 => 25
11000010 => 27
11000011 => 27
11000100 => 27
11000101 => 28
11000110 => 27
11000111 => 28
11001000 => 27
11001001 => 25
11001010 => 27
11001011 => 28
11001100 => 25
11001101 => 27
11001110 => 27
11001111 => 27
11010000 => 27
11010001 => 28
11010010 => 27
11010011 => 28
11010100 => 25
11010101 => 21
11010110 => 25
11010111 => 26
11011000 => 27
11011001 => 27
11011010 => 24
11011011 => 21
11011100 => 27
11011101 => 24
11011110 => 25
11011111 => 24
11100000 => 24
11100001 => 27
11100010 => 28
11100011 => 28
11100100 => 27
11100101 => 28
11100110 => 27
11100111 => 27
11101000 => 28
11101001 => 28
11101010 => 24
11101011 => 26
11101100 => 27
11101101 => 24
11101110 => 24
11101111 => 25
11110000 => 25
11110001 => 27
11110010 => 27
11110011 => 27
11110100 => 27
11110101 => 25
11110110 => 25
11110111 => 25
11111000 => 24
11111001 => 25
11111010 => 24
11111011 => 24
11111100 => 21
11111101 => 21
11111110 => 16
11111111 => 9
000000000 => 10
000000001 => 18
000000010 => 24
000000011 => 24
000000100 => 28
000000101 => 28
000000110 => 29
000000111 => 28
000001000 => 30
000001001 => 30
000001010 => 30
000001011 => 32
000001100 => 32
000001101 => 32
000001110 => 32
000001111 => 30
000010000 => 30
000010001 => 30
000010010 => 30
000010011 => 33
000010100 => 32
000010101 => 30
000010110 => 34
000010111 => 34
000011000 => 33
000011001 => 33
000011010 => 34
000011011 => 33
000011100 => 34
000011101 => 34
000011110 => 33
000011111 => 30
000100000 => 30
000100001 => 30
000100010 => 28
000100011 => 32
000100100 => 28
000100101 => 31
000100110 => 34
000100111 => 34
000101000 => 32
000101001 => 32
000101010 => 28
000101011 => 32
000101100 => 35
000101101 => 34
000101110 => 35
000101111 => 34
000110000 => 33
000110001 => 32
000110010 => 34
000110011 => 32
000110100 => 35
000110101 => 34
000110110 => 32
000110111 => 34
000111000 => 34
000111001 => 34
000111010 => 35
000111011 => 34
000111100 => 34
000111101 => 34
000111110 => 32
000111111 => 28
001000000 => 28
001000001 => 30
001000010 => 30
001000011 => 33
001000100 => 28
001000101 => 31
001000110 => 34
001000111 => 34
001001000 => 28
001001001 => 24
001001010 => 30
001001011 => 32
001001100 => 33
001001101 => 34
001001110 => 34
001001111 => 33
001010000 => 32
001010001 => 32
001010010 => 30
001010011 => 33
001010100 => 28
001010101 => 24
001010110 => 32
001010111 => 32
001011000 => 35
001011001 => 34
001011010 => 33
001011011 => 32
001011100 => 35
001011101 => 34
001011110 => 34
001011111 => 32
001100000 => 32
001100001 => 33
001100010 => 34
001100011 => 32
001100100 => 33
001100101 => 34
001100110 => 29
001100111 => 32
001101000 => 35
001101001 => 34
001101010 => 32
001101011 => 33
001101100 => 32
001101101 => 29
001101110 => 33
001101111 => 33
001110000 => 34
001110001 => 34
001110010 => 34
001110011 => 32
001110100 => 35
001110101 => 34
001110110 => 33
001110111 => 32
001111000 => 34
001111001 => 33
001111010 => 34
001111011 => 33
001111100 => 32
001111101 => 32
001111110 => 29
001111111 => 24
010000000 => 24
010000001 => 28
010000010 => 30
010000011 => 32
010000100 => 30
010000101 => 32
010000110 => 34
010000111 => 34
010001000 => 28
010001001 => 30
010001010 => 32
010001011 => 34
010001100 => 34
010001101 => 35
010001110 => 35
010001111 => 34
010010000 => 30
010010001 => 30
010010010 => 24
010010011 => 29
010010100 => 30
010010101 => 30
010010110 => 34
010010111 => 34
010011000 => 34
010011001 => 32
010011010 => 34
010011011 => 34
010011100 => 34
010011101 => 35
010011110 => 34
010011111 => 32
010100000 => 30
010100001 => 32
010100010 => 32
010100011 => 34
010100100 => 30
010100101 => 30
010100110 => 34
010100111 => 34
010101000 => 28
010101001 => 28
010101010 => 18
010101011 => 24
010101100 => 32
010101101 => 30
010101110 => 31
010101111 => 30
010110000 => 34
010110001 => 35
010110010 => 34
010110011 => 34
010110100 => 33
010110101 => 30
010110110 => 28
010110111 => 31
010111000 => 35
010111001 => 35
010111010 => 32
010111011 => 31
010111100 => 34
010111101 => 32
010111110 => 31
010111111 => 28
011000000 => 29
011000001 => 32
011000010 => 34
011000011 => 33
011000100 => 34
011000101 => 35
011000110 => 32
011000111 => 34
011001000 => 34
011001001 => 32
011001010 => 34
011001011 => 34
011001100 => 29
011001101 => 32
011001110 => 33
011001111 => 33
011010000 => 34
011010001 => 35
011010010 => 34
011010011 => 34
011010100 => 32
011010101 => 28
011010110 => 30
011010111 => 32
011011000 => 32
011011001 => 32
011011010 => 28
011011011 => 24
011011100 => 33
011011101 => 30
011011110 => 31
011011111 => 30
011100000 => 32
011100001 => 34
011100010 => 35
011100011 => 34
011100100 => 34
011100101 => 35
011100110 => 33
011100111 => 32
011101000 => 35
011101001 => 35
011101010 => 31
011101011 => 32
011101100 => 33
011101101 => 30
011101110 => 28
011101111 => 30
011110000 => 33
011110001 => 34
011110010 => 34
011110011 => 33
011110100 => 34
011110101 => 32
011110110 => 31
011110111 => 30
011111000 => 32
011111001 => 32
011111010 => 31
011111011 => 30
011111100 => 29
011111101 => 28
011111110 => 24
011111111 => 18
100000000 => 18
100000001 => 24
100000010 => 28
100000011 => 29
100000100 => 30
100000101 => 31
100000110 => 32
100000111 => 32
100001000 => 30
100001001 => 31
100001010 => 32
100001011 => 34
100001100 => 33
100001101 => 34
100001110 => 34
100001111 => 33
100010000 => 30
100010001 => 28
100010010 => 30
100010011 => 33
100010100 => 32
100010101 => 31
100010110 => 35
100010111 => 35
100011000 => 32
100011001 => 33
100011010 => 35
100011011 => 34
100011100 => 34
100011101 => 35
100011110 => 34
100011111 => 32
100100000 => 30
100100001 => 31
100100010 => 30
100100011 => 33
100100100 => 24
100100101 => 28
100100110 => 32
100100111 => 32
100101000 => 32
100101001 => 30
100101010 => 28
100101011 => 32
100101100 => 34
100101101 => 34
100101110 => 35
100101111 => 34
100110000 => 33
100110001 => 33
100110010 => 32
100110011 => 29
100110100 => 34
100110101 => 34
100110110 => 32
100110111 => 34
100111000 => 34
100111001 => 32
100111010 => 35
100111011 => 34
100111100 => 33
100111101 => 34
100111110 => 32
100111111 => 29
101000000 => 28
101000001 => 31
101000010 => 32
101000011 => 34
101000100 => 31
101000101 => 32
101000110 => 35
101000111 => 35
101001000 => 31
101001001 => 28
101001010 => 30
101001011 => 33
101001100 => 34
101001101 => 34
101001110 => 35
101001111 => 34
101010000 => 30
101010001 => 31
101010010 => 30
101010011 => 32
101010100 => 24
101010101 => 18
101010110 => 28
101010111 => 28
101011000 => 34
101011001 => 34
101011010 => 30
101011011 => 30
101011100 => 34
101011101 => 32
101011110 => 32
101011111 => 30
101100000 => 32
101100001 => 34
101100010 => 35
101100011 => 34
101100100 => 34
101100101 => 34
101100110 => 32
101100111 => 34
101101000 => 34
101101001 => 34
101101010 => 30
101101011 => 30
101101100 => 29
101101101 => 24
101101110 => 30
101101111 => 30
101110000 => 34
101110001 => 35
101110010 => 35
101110011 => 34
101110100 => 34
101110101 => 32
101110110 => 30
101110111 => 28
101111000 => 34
101111001 => 34
101111010 => 32
101111011 => 30
101111100 => 32
101111101 => 30
101111110 => 28
101111111 => 24
110000000 => 24
110000001 => 29
110000010 => 32
110000011 => 32
110000100 => 33
110000101 => 34
110000110 => 33
110000111 => 34
110001000 => 32
110001001 => 33
110001010 => 34
110001011 => 35
110001100 => 32
110001101 => 34
110001110 => 34
110001111 => 34
110010000 => 33
110010001 => 33
110010010 => 29
110010011 => 32
110010100 => 33
110010101 => 32
110010110 => 34
110010111 => 35
110011000 => 32
110011001 => 29
110011010 => 34
110011011 => 33
110011100 => 32
110011101 => 34
110011110 => 33
110011111 => 32
110100000 => 32
110100001 => 34
110100010 => 34
110100011 => 35
110100100 => 32
110100101 => 33
110100110 => 34
110100111 => 35
110101000 => 32
110101001 => 32
110101010 => 24
110101011 => 28
110101100 => 33
110101101 => 30
110101110 => 32
110101111 => 32
110110000 => 33
110110001 => 34
110110010 => 34
110110011 => 33
110110100 => 32
110110101 => 30
110110110 => 24
110110111 => 28
110111000 => 34
110111001 => 34
110111010 => 31
110111011 => 28
110111100 => 33
110111101 => 30
110111110 => 30
110111111 => 28
111000000 => 28
111000001 => 32
111000010 => 34
111000011 => 34
111000100 => 34
111000101 => 35
111000110 => 34
111000111 => 34
111001000 => 34
111001001 => 32
111001010 => 34
111001011 => 35
111001100 => 32
111001101 => 34
111001110 => 32
111001111 => 33
111010000 => 34
111010001 => 35
111010010 => 34
111010011 => 35
111010100 => 32
111010101 => 28
111010110 => 32
111010111 => 32
111011000 => 34
111011001 => 34
111011010 => 31
111011011 => 28
111011100 => 32
111011101 => 28
111011110 => 30
111011111 => 30
111100000 => 30
111100001 => 33
111100010 => 34
111100011 => 34
111100100 => 33
111100101 => 34
111100110 => 33
111100111 => 33
111101000 => 34
111101001 => 34
111101010 => 30
111101011 => 32
111101100 => 33
111101101 => 30
111101110 => 30
111101111 => 30
111110000 => 30
111110001 => 32
111110010 => 32
111110011 => 32
111110100 => 32
111110101 => 30
111110110 => 30
111110111 => 30
111111000 => 28
111111001 => 29
111111010 => 28
111111011 => 28
111111100 => 24
111111101 => 24
111111110 => 18
111111111 => 10
0000000000 => 11
0000000001 => 20
0000000010 => 27
0000000011 => 27
0000000100 => 32
0000000101 => 32
0000000110 => 33
0000000111 => 32
0000001000 => 35
0000001001 => 35
0000001010 => 35
0000001011 => 37
0000001100 => 37
0000001101 => 37
0000001110 => 37
0000001111 => 35
0000010000 => 36
0000010001 => 36
0000010010 => 36
0000010011 => 39
0000010100 => 38
0000010101 => 36
0000010110 => 40
0000010111 => 40
0000011000 => 39
0000011001 => 39
0000011010 => 40
0000011011 => 39
0000011100 => 40
0000011101 => 40
0000011110 => 39
0000011111 => 36
0000100000 => 36
0000100001 => 35
0000100010 => 35
0000100011 => 39
0000100100 => 35
0000100101 => 38
0000100110 => 41
0000100111 => 41
0000101000 => 39
0000101001 => 39
0000101010 => 35
0000101011 => 39
0000101100 => 42
0000101101 => 41
0000101110 => 42
0000101111 => 41
0000110000 => 39
0000110001 => 39
0000110010 => 41
0000110011 => 39
0000110100 => 42
0000110101 => 41
0000110110 => 39
0000110111 => 41
0000111000 => 41
0000111001 => 41
0000111010 => 42
0000111011 => 41
0000111100 => 41
0000111101 => 41
0000111110 => 39
0000111111 => 35
0001000000 => 35
0001000001 => 36
0001000010 => 35
0001000011 => 39
0001000100 => 32
0001000101 => 36
0001000110 => 40
0001000111 => 40
0001001000 => 35
0001001001 => 32
0001001010 => 38
0001001011 => 40
0001001100 => 41
0001001101 => 42
0001001110 => 42
0001001111 => 41
0001010000 => 39
0001010001 => 38
0001010010 => 38
0001010011 => 41
0001010100 => 36
0001010101 => 32
0001010110 => 40
0001010111 => 40
0001011000 => 42
0001011001 => 42
0001011010 => 41
0001011011 => 40
0001011100 => 43
0001011101 => 42
0001011110 => 42
0001011111 => 40
0001100000 => 39
0001100001 => 39
0001100010 => 40
0001100011 => 37
0001100100 => 41
0001100101 => 42
0001100110 => 37
0001100111 => 40
0001101000 => 42
0001101001 => 42
0001101010 => 40
0001101011 => 41
0001101100 => 40
0001101101 => 37
0001101110 => 41
0001101111 => 41
0001110000 => 41
0001110001 => 40
0001110010 => 42
0001110011 => 40
0001110100 => 43
0001110101 => 42
0001110110 => 41
0001110111 => 40
0001111000 => 41
0001111001 => 41
0001111010 => 42
0001111011 => 41
0001111100 => 40
0001111101 => 40
0001111110 => 37
0001111111 => 32
0010000000 => 32
0010000001 => 35
0010000010 => 36
0010000011 => 39
0010000100 => 35
0010000101 => 38
0010000110 => 41
0010000111 => 41
0010001000 => 32
0010001001 => 35
0010001010 => 38
0010001011 => 40
0010001100 => 41
0010001101 => 42
0010001110 => 42
0010001111 => 41
0010010000 => 35
0010010001 => 35
0010010010 => 27
0010010011 => 33
0010010100 => 36
0010010101 => 36
0010010110 => 40
0010010111 => 40
0010011000 => 41
0010011001 => 39
0010011010 => 41
0010011011 => 41
0010011100 => 41
0010011101 => 42
0010011110 => 41
0010011111 => 39
0010100000 => 38
0010100001 => 39
0010100010 => 38
0010100011 => 41
0010100100 => 36
0010100101 => 35
0010100110 => 41
0010100111 => 41
0010101000 => 36
0010101001 => 35
0010101010 => 27
0010101011 => 33
0010101100 => 40
0010101101 => 39
0010101110 => 40
0010101111 => 39
0010110000 => 42
0010110001 => 42
click to show generating function       
Description
The number of distinct factors of a binary word.
This is also known as the subword complexity of a binary word, see [1].
Code
def statistic(x):
    return x.number_of_factors()

Created
Nov 19, 2015 at 12:16 by Martin Rubey
Updated
Jun 03, 2016 at 11:21 by Martin Rubey