A245900 Number of permutations of [n] avoiding 321 that can be realized on increasing unary-binary trees.

1, 1, 2, 4, 10, 27, 79, 239

Offset: 1

Author

Manda Riehl, Aug 06 2014

Keywords

• nonn
• more

Comments

The number of permutations avoiding 321 in the classical sense which can be realized as labels on an increasing unary-binary tree read in the order they appear in a breadth-first search. (Note that breadth-first search reading word is equivalent to reading the tree left to right by levels, starting with the root.)

In some cases, more than one tree results in the same breadth-first search reading word, but here we count the permutations, not the trees.

Examples

			For example, when n=4, a(n)=4. The permutations 1234, 1243, 1324, and 1423 all avoid 321 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes:
       1           1           1           1
      / \         / \         / \         / \
     2   3       2   4       3   2       4   2
     |           |           |               |
     4           3           4               3
		

Crossrefs

Cf. A245903 (odd bisection).

A245890 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.