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BinaryNodes on BinaryTree ​

The number of nodes with two children.

On BinaryTree

Nodes with two children; FindStat calls them branches.

Called as CombinatorialStat(x, "BinaryNodes"). 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 St000196

The number of occurrences of the contiguous pattern [[.,.],[.,.

The number of occurrences of the contiguous pattern {{{[[.,.],[.,.]]}}} in a binary tree.
ObjectValue
[.,.]0
[.,[.,.]]0
[[.,.],.]0
[.,[.,[.,.]]]0
[.,[[.,.],.]]0
[[.,.],[.,.]]1
[[.,[.,.]],.]0
[[[.,.],.],.]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000196 has the rest.