Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001424
(load all 5 compositions to match this statistic)
Mapping
St001424: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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
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.