Identifier
Values
[1,0] => 10 => 2
[1,0,1,0] => 1010 => 6
[1,1,0,0] => 1100 => 4
[1,0,1,0,1,0] => 101010 => 20
[1,0,1,1,0,0] => 101100 => 16
[1,1,0,0,1,0] => 110010 => 14
[1,1,0,1,0,0] => 110100 => 12
[1,1,1,0,0,0] => 111000 => 8
[1,0,1,0,1,0,1,0] => 10101010 => 70
[1,0,1,0,1,1,0,0] => 10101100 => 60
[1,0,1,1,0,0,1,0] => 10110010 => 58
[1,0,1,1,0,1,0,0] => 10110100 => 52
[1,0,1,1,1,0,0,0] => 10111000 => 40
[1,1,0,0,1,0,1,0] => 11001010 => 50
[1,1,0,0,1,1,0,0] => 11001100 => 44
[1,1,0,1,0,0,1,0] => 11010010 => 44
[1,1,0,1,0,1,0,0] => 11010100 => 40
[1,1,0,1,1,0,0,0] => 11011000 => 32
[1,1,1,0,0,0,1,0] => 11100010 => 30
[1,1,1,0,0,1,0,0] => 11100100 => 28
[1,1,1,0,1,0,0,0] => 11101000 => 24
[1,1,1,1,0,0,0,0] => 11110000 => 16
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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 $10\dots 10$.
Map
to binary word
Description
Return the Dyck word as binary word.