[seqfan] Re: Help needed with A007863 Number of hybrid binary trees with n nodes.

Benoît Jubin benoit.jubin at gmail.com
Fri May 18 09:24:59 CEST 2012

Indeed, the definition should be changed too:

A007863 Number of hybrid binary trees with n internal nodes (hence 2n+1 nodes)

and a definition of hybrid binary trees could be add in the comments
(this is the definition used by Pallo in the reference cited there):

An (a,n)-labelled binary tree is a binary tree where each internal
node is labelled by "a" (for associative) or "n" (for nonassociative).
We define on the set of (a,n)-labelled binary trees with m nodes an
equivalence relation as follows: if a tree has an 'a' node A with a
child being also an 'a' node, then if we switch the left and right
subtrees of that node A, we obtain an equivalent tree, and all
equivalent trees are obtained in this way.
A hybrid binary tree is an equivalence class of (a,n)-labelled binary
trees under this relation.


On Thu, May 17, 2012 at 7:31 PM, David Scambler <dscambler at bmm.com> wrote:
> https://oeis.org/A007863
> I am not sure what the hybrid binary trees are.
> For example, what are the 7 trees counted by a(2) = 7?
> Thanks
> dave
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