A245903 Number of permutations of length 2n-1 avoiding 321 that can be realized on increasing binary trees.

1, 2, 10, 79, 753

Offset: 1

Author

Manda Riehl, Aug 22 2014

Keywords

• nonn
• more

Comments

The number of permutations of length 2n-1 avoiding 321 in the classical sense which can be realized as labels on an increasing 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 n=3, the a(3)= 10 permutations can be read from the sample trees given in the Links section above.
		

Links

• Manda Riehl, When n=3, the 10 permutations of length 5 that avoid 321 and can be realized on increasing binary trees.
• Manda Riehl, Maple file used to calculate the terms.

Crossrefs

A245903 appears to be the terms of A245900 with odd indices. A245896 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.