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Identifier
Values
=>
0=>0 1=>0 00=>0 01=>0 10=>0 11=>0 000=>1 001=>0 010=>0 011=>0 100=>0 101=>0 110=>0 111=>1 0000=>1 0001=>1 0010=>0 0011=>0 0100=>0 0101=>0 0110=>0 0111=>1 1000=>1 1001=>0 1010=>0 1011=>0 1100=>0 1101=>0 1110=>1 1111=>1 00000=>1 00001=>1 00010=>1 00011=>1 00100=>0 00101=>0 00110=>0 00111=>1 01000=>1 01001=>0 01010=>0 01011=>0 01100=>0 01101=>0 01110=>1 01111=>1 10000=>1 10001=>1 10010=>0 10011=>0 10100=>0 10101=>0 10110=>0 10111=>1 11000=>1 11001=>0 11010=>0 11011=>0 11100=>1 11101=>1 11110=>1 11111=>1 000000=>2 000001=>1 000010=>1 000011=>1 000100=>1 000101=>1 000110=>1 000111=>2 001000=>1 001001=>0 001010=>0 001011=>0 001100=>0 001101=>0 001110=>1 001111=>1 010000=>1 010001=>1 010010=>0 010011=>0 010100=>0 010101=>1 010110=>0 010111=>1 011000=>1 011001=>0 011010=>0 011011=>0 011100=>1 011101=>1 011110=>1 011111=>1 100000=>1 100001=>1 100010=>1 100011=>1 100100=>0 100101=>0 100110=>0 100111=>1 101000=>1 101001=>0 101010=>1 101011=>0 101100=>0 101101=>0 101110=>1 101111=>1 110000=>1 110001=>1 110010=>0 110011=>0 110100=>0 110101=>0 110110=>0 110111=>1 111000=>2 111001=>1 111010=>1 111011=>1 111100=>1 111101=>1 111110=>1 111111=>2 0000000=>2 0000001=>2 0000010=>1 0000011=>1 0000100=>1 0000101=>1 0000110=>1 0000111=>2 0001000=>1 0001001=>1 0001010=>1 0001011=>1 0001100=>1 0001101=>1 0001110=>2 0001111=>2 0010000=>1 0010001=>1 0010010=>0 0010011=>0 0010100=>0 0010101=>1 0010110=>0 0010111=>1 0011000=>1 0011001=>0 0011010=>0 0011011=>0 0011100=>1 0011101=>1 0011110=>1 0011111=>1 0100000=>1 0100001=>1 0100010=>1 0100011=>1 0100100=>0 0100101=>0 0100110=>0 0100111=>1 0101000=>1 0101001=>0 0101010=>2 0101011=>1 0101100=>0 0101101=>0 0101110=>1 0101111=>1 0110000=>1 0110001=>1 0110010=>0 0110011=>0 0110100=>0 0110101=>0 0110110=>0 0110111=>1 0111000=>2 0111001=>1 0111010=>1 0111011=>1 0111100=>1 0111101=>1 0111110=>1 0111111=>2 1000000=>2 1000001=>1 1000010=>1 1000011=>1 1000100=>1 1000101=>1 1000110=>1 1000111=>2 1001000=>1 1001001=>0 1001010=>0 1001011=>0 1001100=>0 1001101=>0 1001110=>1 1001111=>1 1010000=>1 1010001=>1 1010010=>0 1010011=>0 1010100=>1 1010101=>2 1010110=>0 1010111=>1 1011000=>1 1011001=>0 1011010=>0 1011011=>0 1011100=>1 1011101=>1 1011110=>1 1011111=>1 1100000=>1 1100001=>1 1100010=>1 1100011=>1 1100100=>0 1100101=>0 1100110=>0 1100111=>1 1101000=>1 1101001=>0 1101010=>1 1101011=>0 1101100=>0 1101101=>0 1101110=>1 1101111=>1 1110000=>2 1110001=>2 1110010=>1 1110011=>1 1110100=>1 1110101=>1 1110110=>1 1110111=>1 1111000=>2 1111001=>1 1111010=>1 1111011=>1 1111100=>1 1111101=>1 1111110=>2 1111111=>2 00000000=>2 00000001=>2 00000010=>2 00000011=>2 00000100=>1 00000101=>1 00000110=>1 00000111=>2 00001000=>1 00001001=>1 00001010=>1 00001011=>1 00001100=>1 00001101=>1 00001110=>2 00001111=>2 00010000=>1 00010001=>1 00010010=>1 00010011=>1 00010100=>1 00010101=>2 00010110=>1 00010111=>2 00011000=>1 00011001=>1 00011010=>1 00011011=>1 00011100=>2 00011101=>2 00011110=>2 00011111=>2 00100000=>1 00100001=>1 00100010=>1 00100011=>1 00100100=>0 00100101=>0 00100110=>0 00100111=>1 00101000=>1 00101001=>0 00101010=>2 00101011=>1 00101100=>0 00101101=>0 00101110=>1 00101111=>1 00110000=>1 00110001=>1 00110010=>0 00110011=>0 00110100=>0 00110101=>0 00110110=>0 00110111=>1 00111000=>2 00111001=>1 00111010=>1 00111011=>1 00111100=>1 00111101=>1 00111110=>1 00111111=>2 01000000=>2 01000001=>1 01000010=>1 01000011=>1 01000100=>1 01000101=>1 01000110=>1 01000111=>2 01001000=>1 01001001=>0 01001010=>0 01001011=>0 01001100=>0 01001101=>0 01001110=>1 01001111=>1 01010000=>1 01010001=>1 01010010=>0 01010011=>0 01010100=>2 01010101=>2 01010110=>1 01010111=>2 01011000=>1 01011001=>0 01011010=>0 01011011=>0 01011100=>1 01011101=>1 01011110=>1 01011111=>1 01100000=>1 01100001=>1 01100010=>1 01100011=>1 01100100=>0 01100101=>0 01100110=>0 01100111=>1 01101000=>1 01101001=>0 01101010=>1 01101011=>0 01101100=>0 01101101=>0 01101110=>1 01101111=>1 01110000=>2 01110001=>2 01110010=>1 01110011=>1 01110100=>1 01110101=>1 01110110=>1 01110111=>1 01111000=>2 01111001=>1 01111010=>1 01111011=>1 01111100=>1 01111101=>1 01111110=>2 01111111=>2 10000000=>2 10000001=>2 10000010=>1 10000011=>1 10000100=>1 10000101=>1 10000110=>1 10000111=>2 10001000=>1 10001001=>1 10001010=>1 10001011=>1 10001100=>1 10001101=>1 10001110=>2 10001111=>2 10010000=>1 10010001=>1 10010010=>0 10010011=>0 10010100=>0 10010101=>1 10010110=>0 10010111=>1 10011000=>1 10011001=>0 10011010=>0 10011011=>0 10011100=>1 10011101=>1 10011110=>1 10011111=>1 10100000=>1 10100001=>1 10100010=>1 10100011=>1 10100100=>0 10100101=>0 10100110=>0 10100111=>1 10101000=>2 10101001=>1 10101010=>2 10101011=>2 10101100=>0 10101101=>0 10101110=>1 10101111=>1 10110000=>1 10110001=>1 10110010=>0 10110011=>0 10110100=>0 10110101=>0 10110110=>0 10110111=>1 10111000=>2 10111001=>1 10111010=>1 10111011=>1 10111100=>1 10111101=>1 10111110=>1 10111111=>2 11000000=>2 11000001=>1 11000010=>1 11000011=>1 11000100=>1 11000101=>1 11000110=>1 11000111=>2 11001000=>1 11001001=>0 11001010=>0 11001011=>0 11001100=>0 11001101=>0 11001110=>1 11001111=>1 11010000=>1 11010001=>1 11010010=>0 11010011=>0 11010100=>1 11010101=>2 11010110=>0 11010111=>1 11011000=>1 11011001=>0 11011010=>0 11011011=>0 11011100=>1 11011101=>1 11011110=>1 11011111=>1 11100000=>2 11100001=>2 11100010=>2 11100011=>2 11100100=>1 11100101=>1 11100110=>1 11100111=>1 11101000=>2 11101001=>1 11101010=>2 11101011=>1 11101100=>1 11101101=>1 11101110=>1 11101111=>1 11110000=>2 11110001=>2 11110010=>1 11110011=>1 11110100=>1 11110101=>1 11110110=>1 11110111=>1 11111000=>2 11111001=>1 11111010=>1 11111011=>1 11111100=>2 11111101=>2 11111110=>2 11111111=>2 000000000=>3 000000001=>2 000000010=>2 000000011=>2 000000100=>2 000000101=>2 000000110=>2 000000111=>3 000001000=>1 000001001=>1 000001010=>1 000001011=>1 000001100=>1 000001101=>1 000001110=>2 000001111=>2 000010000=>1 000010001=>1 000010010=>1 000010011=>1 000010100=>1 000010101=>2 000010110=>1 000010111=>2 000011000=>1 000011001=>1 000011010=>1 000011011=>1 000011100=>2 000011101=>2 000011110=>2 000011111=>2 000100000=>1 000100001=>1 000100010=>1 000100011=>1 000100100=>1 000100101=>1 000100110=>1 000100111=>2 000101000=>1 000101001=>1 000101010=>3 000101011=>2 000101100=>1 000101101=>1 000101110=>2 000101111=>2 000110000=>1 000110001=>1 000110010=>1 000110011=>1 000110100=>1 000110101=>1 000110110=>1 000110111=>2 000111000=>2 000111001=>2 000111010=>2 000111011=>2 000111100=>2 000111101=>2 000111110=>2 000111111=>3 001000000=>2 001000001=>1 001000010=>1 001000011=>1 001000100=>1 001000101=>1 001000110=>1 001000111=>2 001001000=>1 001001001=>1 001001010=>0 001001011=>0 001001100=>0 001001101=>0 001001110=>1 001001111=>1 001010000=>1 001010001=>1 001010010=>0 001010011=>0 001010100=>2 001010101=>2 001010110=>1 001010111=>2 001011000=>1 001011001=>0 001011010=>0 001011011=>0 001011100=>1 001011101=>1 001011110=>1 001011111=>1 001100000=>1 001100001=>1 001100010=>1 001100011=>1 001100100=>0 001100101=>0 001100110=>0 001100111=>1 001101000=>1 001101001=>0 001101010=>1 001101011=>0 001101100=>0 001101101=>0 001101110=>1 001101111=>1 001110000=>2 001110001=>2 001110010=>1 001110011=>1 001110100=>1 001110101=>1 001110110=>1 001110111=>1 001111000=>2 001111001=>1 001111010=>1 001111011=>1 001111100=>1 001111101=>1 001111110=>2 001111111=>2 010000000=>2 010000001=>2 010000010=>1 010000011=>1 010000100=>1 010000101=>1 010000110=>1 010000111=>2 010001000=>1 010001001=>1 010001010=>1 010001011=>1 010001100=>1 010001101=>1 010001110=>2 010001111=>2 010010000=>1 010010001=>1 010010010=>1 010010011=>0 010010100=>0 010010101=>1 010010110=>0 010010111=>1 010011000=>1 010011001=>0 010011010=>0 010011011=>0 010011100=>1 010011101=>1 010011110=>1 010011111=>1 010100000=>1 010100001=>1 010100010=>1 010100011=>1 010100100=>0 010100101=>0 010100110=>0 010100111=>1 010101000=>3 010101001=>2 010101010=>2 010101011=>2 010101100=>1 010101101=>1 010101110=>2 010101111=>2 010110000=>1 010110001=>1 010110010=>0 010110011=>0 010110100=>0 010110101=>0 010110110=>0 010110111=>1 010111000=>2 010111001=>1 010111010=>1 010111011=>1 010111100=>1 010111101=>1 010111110=>1 010111111=>2 011000000=>2 011000001=>1 011000010=>1 011000011=>1 011000100=>1 011000101=>1 011000110=>1 011000111=>2 011001000=>1 011001001=>0 011001010=>0 011001011=>0 011001100=>0 011001101=>0 011001110=>1 011001111=>1 011010000=>1 011010001=>1 011010010=>0 011010011=>0 011010100=>1 011010101=>2 011010110=>0 011010111=>1 011011000=>1 011011001=>0 011011010=>0 011011011=>1 011011100=>1 011011101=>1 011011110=>1 011011111=>1 011100000=>2 011100001=>2 011100010=>2 011100011=>2 011100100=>1 011100101=>1 011100110=>1 011100111=>1 011101000=>2 011101001=>1 011101010=>2 011101011=>1 011101100=>1 011101101=>1 011101110=>1 011101111=>1 011110000=>2 011110001=>2 011110010=>1 011110011=>1 011110100=>1 011110101=>1 011110110=>1 011110111=>1 011111000=>2 011111001=>1 011111010=>1 011111011=>1 011111100=>2 011111101=>2 011111110=>2 011111111=>2 100000000=>2 100000001=>2 100000010=>2 100000011=>2 100000100=>1 100000101=>1 100000110=>1 100000111=>2 100001000=>1 100001001=>1 100001010=>1 100001011=>1 100001100=>1 100001101=>1 100001110=>2 100001111=>2 100010000=>1 100010001=>1 100010010=>1 100010011=>1 100010100=>1 100010101=>2 100010110=>1 100010111=>2 100011000=>1 100011001=>1 100011010=>1 100011011=>1 100011100=>2 100011101=>2 100011110=>2 100011111=>2 100100000=>1 100100001=>1 100100010=>1 100100011=>1 100100100=>1 100100101=>0 100100110=>0 100100111=>1 100101000=>1 100101001=>0 100101010=>2 100101011=>1 100101100=>0 100101101=>0 100101110=>1 100101111=>1 100110000=>1 100110001=>1 100110010=>0 100110011=>0 100110100=>0 100110101=>0 100110110=>0 100110111=>1 100111000=>2 100111001=>1 100111010=>1 100111011=>1 100111100=>1 100111101=>1 100111110=>1 100111111=>2 101000000=>2 101000001=>1 101000010=>1 101000011=>1 101000100=>1 101000101=>1 101000110=>1 101000111=>2 101001000=>1 101001001=>0 101001010=>0 101001011=>0 101001100=>0 101001101=>0 101001110=>1 101001111=>1 101010000=>2 101010001=>2 101010010=>1 101010011=>1 101010100=>2 101010101=>2 101010110=>2 101010111=>3 101011000=>1 101011001=>0 101011010=>0 101011011=>0 101011100=>1 101011101=>1 101011110=>1 101011111=>1 101100000=>1 101100001=>1 101100010=>1 101100011=>1 101100100=>0 101100101=>0 101100110=>0 101100111=>1 101101000=>1 101101001=>0 101101010=>1 101101011=>0 101101100=>0 101101101=>1 101101110=>1 101101111=>1 101110000=>2 101110001=>2 101110010=>1 101110011=>1 101110100=>1 101110101=>1 101110110=>1 101110111=>1 101111000=>2 101111001=>1 101111010=>1 101111011=>1 101111100=>1 101111101=>1 101111110=>2 101111111=>2 110000000=>2 110000001=>2 110000010=>1 110000011=>1 110000100=>1 110000101=>1 110000110=>1 110000111=>2 110001000=>1 110001001=>1 110001010=>1 110001011=>1 110001100=>1 110001101=>1 110001110=>2 110001111=>2 110010000=>1 110010001=>1 110010010=>0 110010011=>0 110010100=>0 110010101=>1 110010110=>0 110010111=>1 110011000=>1 110011001=>0 110011010=>0 110011011=>0 110011100=>1 110011101=>1 110011110=>1 110011111=>1 110100000=>1 110100001=>1 110100010=>1 110100011=>1 110100100=>0 110100101=>0 110100110=>0 110100111=>1 110101000=>2 110101001=>1 110101010=>2 110101011=>2 110101100=>0 110101101=>0 110101110=>1 110101111=>1 110110000=>1 110110001=>1 110110010=>0 110110011=>0 110110100=>0 110110101=>0 110110110=>1 110110111=>1 110111000=>2 110111001=>1 110111010=>1 110111011=>1 110111100=>1 110111101=>1 110111110=>1 110111111=>2 111000000=>3 111000001=>2 111000010=>2 111000011=>2 111000100=>2 111000101=>2 111000110=>2 111000111=>2 111001000=>2 111001001=>1 111001010=>1 111001011=>1 111001100=>1 111001101=>1 111001110=>1 111001111=>1 111010000=>2 111010001=>2 111010010=>1 111010011=>1 111010100=>2 111010101=>3 111010110=>1 111010111=>1 111011000=>2 111011001=>1 111011010=>1 111011011=>1 111011100=>1 111011101=>1 111011110=>1 111011111=>1 111100000=>2 111100001=>2 111100010=>2 111100011=>2 111100100=>1 111100101=>1 111100110=>1 111100111=>1 111101000=>2 111101001=>1 111101010=>2 111101011=>1 111101100=>1 111101101=>1 111101110=>1 111101111=>1 111110000=>2 111110001=>2 111110010=>1 111110011=>1 111110100=>1 111110101=>1 111110110=>1 111110111=>1 111111000=>3 111111001=>2 111111010=>2 111111011=>2 111111100=>2 111111101=>2 111111110=>2 111111111=>3
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Description
The number of distinct cubes in a binary word.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uuu$ is a factor of the word.
References
[1] Number of cubefree words of length n on two letters. OEIS:A028445
Code
def statistic(w):
    lst = []
    for i in range(len(w)):
        for l in range(1, (len(w)-i)//3+1):
            if w[i:i+l] == w[i+l:i+2*l] == w[i+2*l:i+3*l]:
                lst.append(tuple(w[i:i+l]))
    return len(set(lst))

Created
Jun 20, 2019 at 00:32 by Martin Rubey
Updated
Jun 20, 2019 at 08:38 by Martin Rubey