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A245893 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word simultaneously avoids 231 and 321. 2
1, 1, 3, 9, 34, 134, 568, 2499 (list; graph; refs; listen; history; text; internal format)



The number of labeled increasing unary-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..8.

Manda Riehl, The nine trees when n = 4.


When n=4, a(n)=9.  In the Links above we show the nine labeled increasing trees on four nodes whose permutation simultaneously avoids 231 and 321.


A245897 gives the number of binary trees instead of unary-binary trees.  A000079 gives the number of permutations which simultaneously avoid 231 and 321 that are breadth-first reading words on labeled increasing unary-binary trees.

Sequence in context: A145090 A273095 A137953 * A085686 A191412 A246013

Adjacent sequences:  A245890 A245891 A245892 * A245894 A245895 A245896




Manda Riehl, Aug 22 2014



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Last modified October 21 18:36 EDT 2021. Contains 348155 sequences. (Running on oeis4.)