WeaklyBelowDyckPathCount on DyckPath

The Dyck paths of the same semilength weakly below this path, itself included.

On DyckPath

Weakly below: each entry of the area sequence is at most this path's.

Called as CombinatorialStat(x, "WeaklyBelowDyckPathCount"). The head's page has its examples.

Live

Distribution

Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.

Sizes 1 to

FindStat St000418

The number of Dyck paths that are weakly below a Dyck path.

Object	Value
[1,0,1,0]	1
[1,1,0,0]	2
[1,0,1,0,1,0]	1
[1,0,1,1,0,0]	2
[1,1,0,0,1,0]	2
[1,1,0,1,0,0]	4
[1,1,1,0,0,0]	5
[1,0,1,0,1,0,1,0]	1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000418 has the rest.