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

Author

Manda Riehl, Aug 19 2014

Keywords

• nonn
• more

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.

Examples

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

Links

• Manda Riehl, The 9 trees when n=4.

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.