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DoubleRisePositionSum on DyckPath ​

The sum of the positions where an up step is followed by an up step.

On DyckPath

Called as CombinatorialStat(x, "DoubleRisePositionSum"). 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 St000976

The sum of the positions of double up-steps 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]3
[1,1,0,0,1,0]1
[1,1,0,1,0,0]1
[1,1,1,0,0,0]3
[1,0,1,0,1,0,1,0]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000976 has the rest.