A245890 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321.

1, 1, 3, 9, 37, 165, 834, 4515

Offset

1,3

Comments

The number of labeled 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 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.

Links

Table of n, a(n) for n=1..8.

Manda Riehl, The 9 trees when n=4.

Example

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

Crossrefs

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 labeled increasing unary-binary trees.

Sequence in context: A321737 A002751 A358397 * A119856 A077365 A366433

Adjacent sequences: A245887 A245888 A245889 * A245891 A245892 A245893

Keyword

nonn,more

Author

Manda Riehl, Aug 19 2014

Status

approved