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RisesOfLengthTwo on DyckPath ​

Rises (maximal runs of up steps) of length 2.

On DyckPath

Called as CombinatorialStat(x, "RisesOfLengthTwo"). 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 St000658

The number of rises of length 2 of a Dyck path.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000658 has the rest.