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A245895 Number of labelled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 312. 3
1, 2, 11, 96, 1093 (list; graph; refs; listen; history; text; internal format)



The number of labelled increasing binary trees with an associated permutation avoiding 312 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).

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 11 labelled trees on 5 nodes whose associated permutation avoids 312.


When n=3, a(n)=11.  In the Links above we show the eleven labelled increasing binary trees on five nodes whose permutation avoids 312.


A245889 gives the number of unary-binary trees instead of binary trees.  A245902 gives the number of permutations which avoid 312 that are breadth-first reading words on labelled increasing binary trees.

Sequence in context: A197994 A186273 A261886 * A231229 A138210 A227465

Adjacent sequences:  A245892 A245893 A245894 * A245896 A245897 A245898




Manda Riehl, Aug 22 2014



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Last modified February 24 21:22 EST 2018. Contains 299628 sequences. (Running on oeis4.)