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Matching statistic: St001365
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Mapping
St001365: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 2
1 => 1
00 => 4
01 => 3
10 => 2
11 => 1
000 => 8
001 => 7
010 => 6
011 => 4
100 => 4
101 => 3
110 => 2
111 => 1
0000 => 16
0001 => 15
0010 => 14
0011 => 11
0100 => 12
0101 => 10
0110 => 8
0111 => 5
1000 => 8
1001 => 7
1010 => 6
1011 => 4
1100 => 4
1101 => 3
1110 => 2
1111 => 1
00000 => 32
00001 => 31
00010 => 30
00011 => 26
00100 => 28
00101 => 25
00110 => 22
00111 => 16
01000 => 24
01001 => 22
01010 => 20
01011 => 15
01100 => 16
01101 => 13
01110 => 10
01111 => 6
10000 => 16
10001 => 15
10010 => 14
10011 => 11
Description
The number of lattice paths of the same length weakly above the path given by a binary word. In particular, there are $2^n$ lattice paths weakly above the the length $n$ binary word $0\dots 0$, there is a unique path weakly above $1\dots 1$, and there are $\binom{2n}{n}$ paths weakly above the length $2n$ binary word $10\dots 10$.