%I
%S 1,2,7,37,222
%N Number of permutations of length 2n1 avoiding 312 that can be realized on increasing binary trees.
%C The number of permutations of length 2n1 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 breadthfirst search. (Note that breadthfirst 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 breadthfirst 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 unarybinary trees whose breadthfirst reading word avoids 312.
%K nonn,more
%O 1,2
%A _Manda Riehl_, Aug 22 2014
