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A245890 Number of labelled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321. 3
1, 1, 3, 9, 37, 165, 834, 4515 (list; graph; refs; listen; history; text; internal format)



The number of labelled increasing unary-binary trees with an associated permutation avoiding 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 9 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 avoids 321.


A245896 gives the number of binary trees instead of unary-binary trees.  A245900 gives the number of permutations which avoid 321 that are breadth-first reading words on labelled increasing unary-binary trees.

Sequence in context: A149022 A134818 A002751 * A119856 A077365 A006229

Adjacent sequences:  A245887 A245888 A245889 * A245891 A245892 A245893




Manda Riehl, Aug 19 2014



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Last modified February 19 16:28 EST 2018. Contains 299356 sequences. (Running on oeis4.)