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
100111=>2
101000=>1
101001=>2
101010=>3
101011=>2
101100=>1
101101=>3
101110=>2
101111=>2
110000=>1
110001=>2
110010=>1
110011=>3
110100=>1
110101=>2
110110=>2
110111=>3
111000=>1
111001=>2
111010=>1
111011=>3
111100=>1
111101=>2
111110=>1
111111=>6
0000000=>7
0000001=>1
0000010=>2
0000011=>1
0000100=>3
0000101=>1
0000110=>2
0000111=>1
0001000=>4
0001001=>1
0001010=>2
0001011=>1
0001100=>3
0001101=>1
0001110=>2
0001111=>1
0010000=>3
0010001=>2
0010010=>3
0010011=>1
0010100=>3
0010101=>1
0010110=>2
0010111=>1
0011000=>3
0011001=>2
0011010=>2
0011011=>1
0011100=>3
0011101=>1
0011110=>2
0011111=>1
0100000=>2
0100001=>2
0100010=>3
0100011=>1
0100100=>3
0100101=>2
0100110=>2
0100111=>1
0101000=>2
0101001=>2
0101010=>4
0101011=>1
0101100=>2
0101101=>2
0101110=>2
0101111=>1
0110000=>2
0110001=>2
0110010=>2
0110011=>2
0110100=>2
0110101=>2
0110110=>3
0110111=>1
0111000=>2
0111001=>2
0111010=>2
0111011=>2
0111100=>2
0111101=>2
0111110=>2
0111111=>1
1000000=>1
1000001=>2
1000010=>2
1000011=>2
1000100=>2
1000101=>2
1000110=>2
1000111=>2
1001000=>1
1001001=>3
1001010=>2
1001011=>2
1001100=>2
1001101=>2
1001110=>2
1001111=>2
1010000=>1
1010001=>2
1010010=>2
1010011=>2
1010100=>1
1010101=>4
1010110=>2
1010111=>2
1011000=>1
1011001=>2
1011010=>2
1011011=>3
1011100=>1
1011101=>3
1011110=>2
1011111=>2
1100000=>1
1100001=>2
1100010=>1
1100011=>3
1100100=>1
1100101=>2
1100110=>2
1100111=>3
1101000=>1
1101001=>2
1101010=>1
1101011=>3
1101100=>1
1101101=>3
1101110=>2
1101111=>3
1110000=>1
1110001=>2
1110010=>1
1110011=>3
1110100=>1
1110101=>2
1110110=>1
1110111=>4
1111000=>1
1111001=>2
1111010=>1
1111011=>3
1111100=>1
1111101=>2
1111110=>1
1111111=>7
00000000=>8
00000001=>1
00000010=>2
00000011=>1
00000100=>3
00000101=>1
00000110=>2
00000111=>1
00001000=>4
00001001=>1
00001010=>2
00001011=>1
00001100=>3
00001101=>1
00001110=>2
00001111=>1
00010000=>4
00010001=>2
00010010=>2
00010011=>1
00010100=>3
00010101=>1
00010110=>2
00010111=>1
00011000=>4
00011001=>1
00011010=>2
00011011=>1
00011100=>3
00011101=>1
00011110=>2
00011111=>1
00100000=>3
00100001=>2
00100010=>3
00100011=>1
00100100=>4
00100101=>1
00100110=>2
00100111=>1
00101000=>3
00101001=>2
00101010=>2
00101011=>1
00101100=>3
00101101=>1
00101110=>2
00101111=>1
00110000=>3
00110001=>2
00110010=>2
00110011=>2
00110100=>3
00110101=>1
00110110=>2
00110111=>1
00111000=>3
00111001=>2
00111010=>2
00111011=>1
00111100=>3
00111101=>1
00111110=>2
00111111=>1
01000000=>2
01000001=>2
01000010=>3
01000011=>1
01000100=>3
01000101=>2
01000110=>2
01000111=>1
01001000=>2
01001001=>3
01001010=>3
01001011=>1
01001100=>2
01001101=>2
01001110=>2
01001111=>1
01010000=>2
01010001=>2
01010010=>3
01010011=>1
01010100=>2
01010101=>4
01010110=>2
01010111=>1
01011000=>2
01011001=>2
01011010=>3
01011011=>1
01011100=>2
01011101=>2
01011110=>2
01011111=>1
01100000=>2
01100001=>2
01100010=>2
01100011=>2
01100100=>2
01100101=>2
01100110=>3
01100111=>1
01101000=>2
01101001=>2
01101010=>2
01101011=>2
01101100=>2
01101101=>3
01101110=>2
01101111=>1
01110000=>2
01110001=>2
01110010=>2
01110011=>2
01110100=>2
01110101=>2
01110110=>2
01110111=>2
01111000=>2
01111001=>2
01111010=>2
01111011=>2
01111100=>2
01111101=>2
01111110=>2
01111111=>1
10000000=>1
10000001=>2
10000010=>2
10000011=>2
10000100=>2
10000101=>2
10000110=>2
10000111=>2
10001000=>2
10001001=>2
10001010=>2
10001011=>2
10001100=>2
10001101=>2
10001110=>2
10001111=>2
10010000=>1
10010001=>2
10010010=>3
10010011=>2
10010100=>2
10010101=>2
10010110=>2
10010111=>2
10011000=>1
10011001=>3
10011010=>2
10011011=>2
10011100=>2
10011101=>2
10011110=>2
10011111=>2
10100000=>1
10100001=>2
10100010=>2
10100011=>2
10100100=>1
10100101=>3
10100110=>2
10100111=>2
10101000=>1
10101001=>2
10101010=>4
10101011=>2
10101100=>1
10101101=>3
10101110=>2
10101111=>2
10110000=>1
10110001=>2
10110010=>2
10110011=>2
10110100=>1
10110101=>3
10110110=>3
10110111=>2
10111000=>1
10111001=>2
10111010=>2
10111011=>3
10111100=>1
10111101=>3
10111110=>2
10111111=>2
11000000=>1
11000001=>2
11000010=>1
11000011=>3
11000100=>1
11000101=>2
11000110=>2
11000111=>3
11001000=>1
11001001=>2
11001010=>1
11001011=>3
11001100=>2
11001101=>2
11001110=>2
11001111=>3
11010000=>1
11010001=>2
11010010=>1
11010011=>3
11010100=>1
11010101=>2
11010110=>2
11010111=>3
11011000=>1
11011001=>2
11011010=>1
11011011=>4
11011100=>1
11011101=>3
11011110=>2
11011111=>3
11100000=>1
11100001=>2
11100010=>1
11100011=>3
11100100=>1
11100101=>2
11100110=>1
11100111=>4
11101000=>1
11101001=>2
11101010=>1
11101011=>3
11101100=>1
11101101=>2
11101110=>2
11101111=>4
11110000=>1
11110001=>2
11110010=>1
11110011=>3
11110100=>1
11110101=>2
11110110=>1
11110111=>4
11111000=>1
11111001=>2
11111010=>1
11111011=>3
11111100=>1
11111101=>2
11111110=>1
11111111=>8
000000000=>9
000000001=>1
000000010=>2
000000011=>1
000000100=>3
000000101=>1
000000110=>2
000000111=>1
000001000=>4
000001001=>1
000001010=>2
000001011=>1
000001100=>3
000001101=>1
000001110=>2
000001111=>1
000010000=>5
000010001=>1
000010010=>2
000010011=>1
000010100=>3
000010101=>1
000010110=>2
000010111=>1
000011000=>4
000011001=>1
000011010=>2
000011011=>1
000011100=>3
000011101=>1
000011110=>2
000011111=>1
000100000=>4
000100001=>2
000100010=>3
000100011=>1
000100100=>3
000100101=>1
000100110=>2
000100111=>1
000101000=>4
000101001=>1
000101010=>2
000101011=>1
000101100=>3
000101101=>1
000101110=>2
000101111=>1
000110000=>4
000110001=>2
000110010=>2
000110011=>1
000110100=>3
000110101=>1
000110110=>2
000110111=>1
000111000=>4
000111001=>1
000111010=>2
000111011=>1
000111100=>3
000111101=>1
000111110=>2
000111111=>1
001000000=>3
001000001=>2
001000010=>3
001000011=>1
001000100=>4
001000101=>1
001000110=>2
001000111=>1
001001000=>3
001001001=>3
001001010=>2
001001011=>1
001001100=>3
001001101=>1
001001110=>2
001001111=>1
001010000=>3
001010001=>2
001010010=>3
001010011=>1
001010100=>3
001010101=>1
001010110=>2
001010111=>1
001011000=>3
001011001=>2
001011010=>2
001011011=>1
001011100=>3
001011101=>1
001011110=>2
001011111=>1
001100000=>3
001100001=>2
001100010=>2
001100011=>2
001100100=>3
001100101=>1
001100110=>3
001100111=>1
001101000=>3
001101001=>2
001101010=>2
001101011=>1
001101100=>3
001101101=>1
001101110=>2
001101111=>1
001110000=>3
001110001=>2
001110010=>2
001110011=>2
001110100=>3
001110101=>1
001110110=>2
001110111=>1
001111000=>3
001111001=>2
001111010=>2
001111011=>1
001111100=>3
001111101=>1
001111110=>2
001111111=>1
010000000=>2
010000001=>2
010000010=>3
010000011=>1
010000100=>3
010000101=>2
010000110=>2
010000111=>1
010001000=>3
010001001=>2
010001010=>3
010001011=>1
010001100=>2
010001101=>2
010001110=>2
010001111=>1
010010000=>2
010010001=>2
010010010=>4
010010011=>1
010010100=>3
010010101=>2
010010110=>2
010010111=>1
010011000=>2
010011001=>2
010011010=>3
010011011=>1
010011100=>2
010011101=>2
010011110=>2
010011111=>1
010100000=>2
010100001=>2
010100010=>3
010100011=>1
010100100=>2
010100101=>3
010100110=>2
010100111=>1
010101000=>2
010101001=>2
010101010=>5
010101011=>1
010101100=>2
010101101=>2
010101110=>2
010101111=>1
010110000=>2
010110001=>2
010110010=>3
010110011=>1
010110100=>2
010110101=>3
010110110=>2
010110111=>1
010111000=>2
010111001=>2
010111010=>3
010111011=>1
010111100=>2
010111101=>2
010111110=>2
010111111=>1
011000000=>2
011000001=>2
011000010=>2
011000011=>2
011000100=>2
011000101=>2
011000110=>3
011000111=>1
011001000=>2
011001001=>2
011001010=>2
011001011=>2
011001100=>3
011001101=>2
011001110=>2
011001111=>1
011010000=>2
011010001=>2
011010010=>2
011010011=>2
011010100=>2
011010101=>2
011010110=>3
011010111=>1
011011000=>2
011011001=>2
011011010=>2
011011011=>3
011011100=>2
011011101=>2
011011110=>2
011011111=>1
011100000=>2
011100001=>2
011100010=>2
011100011=>2
011100100=>2
011100101=>2
011100110=>2
011100111=>2
011101000=>2
011101001=>2
011101010=>2
011101011=>2
011101100=>2
011101101=>2
011101110=>3
011101111=>1
011110000=>2
011110001=>2
011110010=>2
011110011=>2
011110100=>2
011110101=>2
011110110=>2
011110111=>2
011111000=>2
011111001=>2
011111010=>2
011111011=>2
011111100=>2
011111101=>2
011111110=>2
011111111=>1
100000000=>1
100000001=>2
100000010=>2
100000011=>2
100000100=>2
100000101=>2
100000110=>2
100000111=>2
100001000=>2
100001001=>2
100001010=>2
100001011=>2
100001100=>2
100001101=>2
100001110=>2
100001111=>2
100010000=>1
100010001=>3
100010010=>2
100010011=>2
100010100=>2
100010101=>2
100010110=>2
100010111=>2
100011000=>2
100011001=>2
100011010=>2
100011011=>2
100011100=>2
100011101=>2
100011110=>2
100011111=>2
100100000=>1
100100001=>2
100100010=>2
100100011=>2
100100100=>3
100100101=>2
100100110=>2
100100111=>2
100101000=>1
100101001=>3
100101010=>2
100101011=>2
100101100=>2
100101101=>2
100101110=>2
100101111=>2
100110000=>1
100110001=>2
100110010=>2
100110011=>3
100110100=>2
100110101=>2
100110110=>2
100110111=>2
100111000=>1
100111001=>3
100111010=>2
100111011=>2
100111100=>2
100111101=>2
100111110=>2
100111111=>2
101000000=>1
101000001=>2
101000010=>2
101000011=>2
101000100=>1
101000101=>3
101000110=>2
101000111=>2
101001000=>1
101001001=>2
101001010=>3
101001011=>2
101001100=>1
101001101=>3
101001110=>2
101001111=>2
101010000=>1
101010001=>2
101010010=>2
101010011=>2
101010100=>1
101010101=>5
101010110=>2
101010111=>2
101011000=>1
101011001=>2
101011010=>3
101011011=>2
101011100=>1
101011101=>3
101011110=>2
101011111=>2
101100000=>1
101100001=>2
101100010=>2
101100011=>2
101100100=>1
101100101=>3
101100110=>2
101100111=>2
101101000=>1
101101001=>2
101101010=>2
101101011=>3
101101100=>1
101101101=>4
101101110=>2
101101111=>2
101110000=>1
101110001=>2
101110010=>2
101110011=>2
101110100=>1
101110101=>3
101110110=>2
101110111=>3
101111000=>1
101111001=>2
101111010=>2
101111011=>3
101111100=>1
101111101=>3
101111110=>2
101111111=>2
110000000=>1
110000001=>2
110000010=>1
110000011=>3
110000100=>1
110000101=>2
110000110=>2
110000111=>3
110001000=>1
110001001=>2
110001010=>1
110001011=>3
110001100=>2
110001101=>2
110001110=>2
110001111=>3
110010000=>1
110010001=>2
110010010=>1
110010011=>3
110010100=>1
110010101=>2
110010110=>2
110010111=>3
110011000=>1
110011001=>3
110011010=>1
110011011=>3
110011100=>2
110011101=>2
110011110=>2
110011111=>3
110100000=>1
110100001=>2
110100010=>1
110100011=>3
110100100=>1
110100101=>2
110100110=>2
110100111=>3
110101000=>1
110101001=>2
110101010=>1
110101011=>3
110101100=>1
110101101=>3
110101110=>2
110101111=>3
110110000=>1
110110001=>2
110110010=>1
110110011=>3
110110100=>1
110110101=>2
110110110=>3
110110111=>3
110111000=>1
110111001=>2
110111010=>1
110111011=>4
110111100=>1
110111101=>3
110111110=>2
110111111=>3
111000000=>1
111000001=>2
111000010=>1
111000011=>3
111000100=>1
111000101=>2
111000110=>1
111000111=>4
111001000=>1
111001001=>2
111001010=>1
111001011=>3
111001100=>1
111001101=>2
111001110=>2
111001111=>4
111010000=>1
111010001=>2
111010010=>1
111010011=>3
111010100=>1
111010101=>2
111010110=>1
111010111=>4
111011000=>1
111011001=>2
111011010=>1
111011011=>3
111011100=>1
111011101=>3
111011110=>2
111011111=>4
111100000=>1
111100001=>2
111100010=>1
111100011=>3
111100100=>1
111100101=>2
111100110=>1
111100111=>4
111101000=>1
111101001=>2
111101010=>1
111101011=>3
111101100=>1
111101101=>2
111101110=>1
111101111=>5
111110000=>1
111110001=>2
111110010=>1
111110011=>3
111110100=>1
111110101=>2
111110110=>1
111110111=>4
111111000=>1
111111001=>2
111111010=>1
111111011=>3
111111100=>1
111111101=>2
111111110=>1
111111111=>9
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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 $w$.
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
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