A245888 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 231.

1, 1, 3, 9, 36, 155, 752, 3894

Offset: 1

Author

Manda Riehl, Aug 18 2014

Keywords

• nonn
• more

Comments

The number of labeled increasing unary-binary trees with an associated permutation avoiding 231 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

			The a(4) = 9 such trees are:
:
:    1             1             1                1
:   /\            /\            /\               /\
:  2  3          2  3          3  2             3  2
:     |          |             |                   |
:     4          4             4                   4
:
:
:     1               1               1          1          1
:    /\              /\               |          |          |
:   2  4            4  2              2          2          2
:   |                  |             /\         /\          |
:   3                  3            3  4       4  3         3
:                                                           |
:                                                           4
:
		

Links

• Manda Riehl, The 9 trees when n = 4.

Crossrefs

A245894 gives the number of such binary trees instead of unary-binary trees.

A245898 gives the number of permutations which avoid 231 that are breadth-first reading words on labeled increasing unary-binary trees instead of the number of trees.