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%I #11 Sep 08 2014 08:46:49
%S 1,2,14,163,2558
%N Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 231.
%C The number of labeled increasing binary trees with an associated permutation avoiding 231 in the classical sense. The tree’s permutation is found by recording the labels in the order 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="/A245894/a245894.png">For n = 3: the 14 labeled trees on 5 nodes whose associated permutation avoids 231. </a>
%e When n=3, a(n)=14. In the Links above we show the fourteen labeled increasing binary trees on five nodes whose permutation avoids 231.
%Y A245888 gives the number of unary-binary trees instead of binary trees.
%Y A245901 gives the number of permutations which avoid 231 that are breadth-first reading words on labeled increasing binary trees.
%K nonn,more
%O 1,2
%A _Manda Riehl_, Aug 22 2014
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