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A245893 Number of labelled 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 labelled 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 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 labelled 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 labelled 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 February 24 17:22 EST 2018. Contains 299624 sequences. (Running on oeis4.)