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RightForkRightLeftPatternCount on BinaryTree ​

The number of nodes whose right child has two children, the right one of which has a left child.

On BinaryTree

FindStat's St000130: the contiguous pattern [.,[[.,.],[[.,.],.]]], whose empty slots match any subtree.

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

Live

Distribution

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

FindStat St000130

The number of occurrences of the contiguous pattern [.,[[.,.],[[.,.],.]]] in a binary tree.

The number of occurrences of the contiguous pattern {{{[.,[[.,.],[[.,.],.]]]}}} in a binary tree.
ObjectValue
[.,.]0
[.,[.,.]]0
[[.,.],.]0
[.,[.,[.,.]]]0
[.,[[.,.],.]]0
[[.,.],[.,.]]0
[[.,[.,.]],.]0
[[[.,.],.],.]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000130 has the rest.