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BoundaryLengthBeyondTrunk on OrderedTree ​

The edges on the leftmost path or the rightmost path from the root, less the trunk they share.

On OrderedTree

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

Live

Distribution

Over OrderedTrees at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St000975

The length of the boundary minus the length of the trunk of an ordered tree.

ObjectValue
[[]]1
[[[]]]2
[[],[]]2
[[[[]]]]3
[[[],[]]]3
[[[]],[]]3
[[],[[]]]3
[[[[[]]]]]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000975 has the rest.