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Identifier

St001884: Binary words ⟶ ℤ

Values

0 => 1

1 => 1

00 => 2

01 => 1

10 => 1

11 => 2

000 => 3

001 => 1

010 => 2

011 => 1

100 => 1

101 => 2

110 => 1

111 => 3

0000 => 4

0001 => 1

0010 => 2

0011 => 1

0100 => 2

0101 => 2

0110 => 2

0111 => 1

1000 => 1

1001 => 2

1010 => 2

1011 => 2

1100 => 1

1101 => 2

1110 => 1

1111 => 4

00000 => 5

00001 => 1

00010 => 2

00011 => 1

00100 => 3

00101 => 1

00110 => 2

00111 => 1

01000 => 2

01001 => 2

01010 => 3

01011 => 1

01100 => 2

01101 => 2

01110 => 2

01111 => 1

10000 => 1

10001 => 2

10010 => 2

10011 => 2

10100 => 1

10101 => 3

10110 => 2

10111 => 2

11000 => 1

11001 => 2

11010 => 1

11011 => 3

11100 => 1

11101 => 2

11110 => 1

11111 => 5

000000 => 6

000001 => 1

000010 => 2

000011 => 1

000100 => 3

000101 => 1

000110 => 2

000111 => 1

001000 => 3

001001 => 2

001010 => 2

001011 => 1

001100 => 3

001101 => 1

001110 => 2

001111 => 1

010000 => 2

010001 => 2

010010 => 3

010011 => 1

010100 => 2

010101 => 3

010110 => 2

010111 => 1

011000 => 2

011001 => 2

011010 => 2

011011 => 2

011100 => 2

011101 => 2

011110 => 2

011111 => 1

100000 => 1

100001 => 2

100010 => 2

100011 => 2

100100 => 2

100101 => 2

100110 => 2

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Description

The number of borders of a binary word.
A border of a binary word $w$ is a word which is both a prefix and a suffix of $w$.

Code

def statistic(w):
    return sum(1 for i in range(1, len(w)+1) if w[:i] == w[-i:])

Created

Dec 21, 2022 at 10:52 by Martin Rubey

Updated

Dec 21, 2022 at 10:52 by Martin Rubey