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%I #14 Jun 03 2018 03:40:49
%S 1,2,10,79,753
%N Number of permutations of length 2n-1 avoiding 321 that can be realized on increasing binary trees.
%C The number of permutations of length 2n-1 avoiding 321 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="/A245903/a245903.png">When n=3, the 10 permutations of length 5 that avoid 321 and can be realized on increasing binary trees.</a>
%H Manda Riehl, <a href="/A245903/a245903.txt">Maple file used to calculate the terms.</a>
%e For n=3, the a(3)= 10 permutations can be read from the sample trees given in the Links section above.
%Y A245903 appears to be the terms of A245900 with odd indices. A245896 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.
%K nonn,more
%O 1,2
%A _Manda Riehl_, Aug 22 2014
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