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A245897 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word simultaneously avoids 231 and 321. 2
1, 2, 12, 98, 940 (list; graph; refs; listen; history; text; internal format)



The number of labeled increasing binary trees with an associated permutation simultaneously avoiding 231 and 321 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.)

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.


Table of n, a(n) for n=1..5.

Manda Riehl, For n = 3: the 12 labelled trees on 5 nodes whose associated permutation simultaneously avoids 231 and 321.


When n=3, a(n)=12.  In the Links above we show the twelve labeled increasing binary trees on five nodes whose permutation simultaneously avoids 231 and 321.


A245893 gives the number of unary-binary trees instead of binary trees.  A081294 gives the number of permutations which simultaneously avoid 231 and 321 that are breadth-first reading words on labeled increasing binary trees.

Sequence in context: A059864 A095338 A219538 * A231173 A303203 A012548

Adjacent sequences:  A245894 A245895 A245896 * A245898 A245899 A245900




Manda Riehl, Aug 22 2014



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Last modified November 19 12:38 EST 2018. Contains 317351 sequences. (Running on oeis4.)