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%I #21 Jun 03 2018 03:39:31
%S 1,1,2,4,10,26,74,217
%N Number of permutations avoiding 231 that can be realized on increasing unary-binary trees with n nodes.
%C The number of permutations avoiding 231 in the classical sense which can be realized as labels on an increasing unary-binary tree with n nodes 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.
%e For example, when n=4, the permutations 1234, 1243, 1324, and 1423 all avoid 231 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes:
%e 1 1 1 1
%e / \ / \ / \ / \
%e 2 3 2 4 3 2 4 2
%e | | | |
%e 4 3 4 3
%Y A245901 is the terms of A245898 with odd indices. A245888 is the number of increasing unary-binary trees whose breadth-first reading word avoids 231.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 05 2014
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