%N Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 312.
%C The number of labeled increasing binary trees with an associated permutation avoiding 312 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="/A245895/a245895.png">For n = 3: the 11 labeled trees on 5 nodes whose associated permutation avoids 312.</a>
%e When n=3, a(n)=11. In the Links above we show the eleven labeled increasing binary trees on five nodes whose permutation avoids 312.
%Y A245889 gives the number of unary-binary trees instead of binary trees. A245902 gives the number of permutations which avoid 312 that are breadth-first reading words on labeled increasing binary trees.
%A _Manda Riehl_, Aug 22 2014