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%I #10 Mar 18 2018 17:32:20
%S 1,1,3,9,37,165,834,4515
%N Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321.
%C The number of labeled increasing unary-binary trees with an associated permutation avoiding 321 in the classical sense. The tree's permutation is found by recording the labels in the order in which they appear in a breadth-first search. (Note that a breadth-first search reading word is equivalent to reading the tree labels left to right by levels, starting with the root.)
%C In some cases, the same breadth-first search reading permutation can be found on differently shaped trees. This sequence gives the number of trees, not the number of permutations.
%H Manda Riehl, <a href="/A245890/a245890.png">The 9 trees when n=4.</a>
%e When n=4, a(n)=9. In the Links above we show the nine labeled increasing trees on four nodes whose permutation avoids 321.
%Y A245896 gives the number of binary trees instead of unary-binary trees. A245900 gives the number of permutations which avoid 321 that are breadth-first reading words on labeled increasing unary-binary trees.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 19 2014
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