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

Created
Jun 20, 2019 at 00:28 by Martin Rubey
Updated
Jun 20, 2019 at 08:39 by Martin Rubey