UpStepsAtOddPositions on DyckPath

Up steps at an odd position, counting from 1.

On DyckPath

Called as CombinatorialStat(x, "UpStepsAtOddPositions"). 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 St000676

The number of odd rises of a Dyck path.

Object	Value
[]	0
[1,0]	1
[1,0,1,0]	2
[1,1,0,0]	1
[1,0,1,0,1,0]	3
[1,0,1,1,0,0]	2
[1,1,0,0,1,0]	2
[1,1,0,1,0,0]	1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000676 has the rest.