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%I #23 Mar 18 2018 17:38:33
%S 1,1,3,9,36,155,752,3894
%N Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 231.
%C The number of labeled increasing unary-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 in which 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="/A245888/a245888.png">The 9 trees when n = 4.</a>
%e The a(4) = 9 such trees are:
%e :
%e : 1 1 1 1
%e : /\ /\ /\ /\
%e : 2 3 2 3 3 2 3 2
%e : | | | |
%e : 4 4 4 4
%e :
%e :
%e : 1 1 1 1 1
%e : /\ /\ | | |
%e : 2 4 4 2 2 2 2
%e : | | /\ /\ |
%e : 3 3 3 4 4 3 3
%e : |
%e : 4
%e :
%Y A245894 gives the number of such binary trees instead of unary-binary trees.
%Y A245898 gives the number of permutations which avoid 231 that are breadth-first reading words on labeled increasing unary-binary trees instead of the number of trees.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 18 2014
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