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RisesOfLengthOneAtOddHeight on DyckPath ​

Rises of length 1 that start at an odd height.

On DyckPath

Called as CombinatorialStat(x, "RisesOfLengthOneAtOddHeight"). 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.

FindStat St001172

The number of 1-rises at odd height of a Dyck path.

ObjectValue
[1,0]0
[1,0,1,0]0
[1,1,0,0]0
[1,0,1,0,1,0]0
[1,0,1,1,0,0]0
[1,1,0,0,1,0]0
[1,1,0,1,0,0]1
[1,1,1,0,0,0]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001172 has the rest.