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A245891 Number of labelled 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 labelled 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 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 labelled 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 labelled 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 February 25 12:34 EST 2018. Contains 299654 sequences. (Running on oeis4.)