%N Number of permutations of length 2n-1 avoiding 312 that can be realized on increasing binary trees.
%C The number of permutations of length 2n-1 avoiding 312 in the classical sense which can be realized as labels on an increasing binary tree read in the order they appear in a breadth-first search. (Note that breadth-first search reading word is equivalent to reading the tree left to right by levels, starting with the root.)
%C In some cases, more than one tree results in the same breadth-first search reading word, but here we count the permutations, not the trees.
%H Manda Riehl, <a href="/A245902/a245902.png">When n=3, the 7 permutations of length 5 that avoid 312 and can be realized on increasing binary trees.</a>
%e For n=3, the a(3)= 7 permutations can be read from the sample trees given in the Links section above.
%Y A245902 appears to be the terms of A245899 with odd indices. A245895 is the number of increasing unary-binary trees whose breadth-first reading word avoids 312.
%A _Manda Riehl_, Aug 22 2014