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UnaryNodes on BinaryTree ​

The number of nodes with exactly one child.

On BinaryTree

Called as CombinatorialStat(x, "UnaryNodes"). 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 St000385

The number of vertices with out-degree 1 in a binary tree.

ObjectValue
[.,[.,.]]1
[[.,.],.]1
[.,[.,[.,.]]]2
[.,[[.,.],.]]2
[[.,.],[.,.]]0
[[.,[.,.]],.]2
[[[.,.],.],.]2
[.,[.,[.,[.,.]]]]3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000385 has the rest.