%I #12 Mar 18 2018 17:31:25
%S 1,1,3,8,28,102,407,1701
%N Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word simultaneously avoids 231 and 312 (or avoids 312 and 321).
%C The number of labeled increasing unary-binary trees with an associated permutation avoiding 231 and 312 simultaneously (or avoids 312 and 321 simultaneously) 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="/A245892/a245892.png">The eight trees when n=4.</a>
%e When n=4, a(n)=8. In the Links above we show the eight labeled increasing trees on four nodes whose permutation simultaneously avoids 231 and 312.
%Y A111554 gives the number of binary trees instead of unary-binary trees.
%Y A002083 gives the number of permutations which avoid 231 and 312 simultaneously that are breadth-first reading words on labeled increasing unary-binary trees.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 19 2014