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A245891 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 213 and 321. 1
1, 1, 3, 7, 20, 55, 157, 448 (list; graph; refs; listen; history; text; internal format)



The number of labeled increasing unary-binary trees with an associated permutation avoiding 213 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..8.

Manda Riehl, The 7 trees when n = 4.


When n=4, a(n)=7.  In the Links above we show the seven labeled increasing trees on four nodes whose permutation avoids 213 and 321.


A126223 gives the number of binary trees instead of unary-binary trees.  A033638 gives the number of permutations which avoid 213 and 321 that are breadth-first reading words on labeled increasing unary-binary trees.

Sequence in context: A293740 A293110 A000227 * A058737 A274478 A238124

Adjacent sequences:  A245888 A245889 A245890 * A245892 A245893 A245894




Manda Riehl, Aug 19 2014



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Last modified November 14 12:36 EST 2018. Contains 317185 sequences. (Running on oeis4.)