%I #9 Mar 18 2018 17:31:00
%S 1,1,3,9,34,134,568,2499
%N Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word simultaneously avoids 231 and 321.
%C The number of labeled increasing unary-binary trees with an associated permutation simultaneously avoiding 231 and 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="/A245893/a245893.png">The nine 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 simultaneously avoids 231 and 321.
%Y A245897 gives the number of binary trees instead of unary-binary trees. A000079 gives the number of permutations which simultaneously avoid 231 and 321 that are breadth-first reading words on labeled increasing unary-binary trees.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 22 2014