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Matching statistic: St001885
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Mapping
St001885: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 2
1 => 2
00 => 1
01 => 2
10 => 2
11 => 1
000 => 1
001 => 4
010 => 1
011 => 4
100 => 4
101 => 1
110 => 4
111 => 1
0000 => 1
0001 => 6
0010 => 3
0011 => 6
0100 => 3
0101 => 1
0110 => 3
0111 => 6
1000 => 6
1001 => 3
1010 => 1
1011 => 3
1100 => 6
1101 => 3
1110 => 6
1111 => 1
00000 => 1
00001 => 12
00010 => 5
00011 => 12
00100 => 1
00101 => 12
00110 => 5
00111 => 12
01000 => 5
01001 => 2
01010 => 1
01011 => 12
01100 => 5
01101 => 2
01110 => 5
01111 => 12
10000 => 12
10001 => 5
10010 => 2
10011 => 5
Description
The number of binary words with the same proper border set. The proper border set of a binary word $w$ is the set of proper prefixes which are also suffixes of $w$. For example, $0010000010$, $0010100010$ and $0010110010$ are the words with proper border set $\{0, 0010\}$, whereas $0010010010$ has proper border set $\{0, 0010, 0010010\}$.