A246747 The number of binary heaps on n elements whose breadth-first search reading word avoids 231.

1, 1, 1, 2, 3, 7, 14, 37, 80, 222, 544, 1601, 4095, 12416, 33785, 105769, 293747, 935184, 2717376, 8848014, 26134254, 86210716, 262068267, 877833206, 2695238060, 9109101156, 28619396967, 97879220771, 310021153392, 1067906857449, 3440140082033, 11957123227292

Offset: 0

Author

Manda Riehl, Sep 04 2014

Keywords

• nonn

Comments

Also, the number of binary heaps on n elements whose breadth-first search reading word avoids 312.

Note that a breadth-first search reading word is equivalent to reading the tree labels left to right by levels, starting with the root.

For more information on heaps, see A056971.

Examples

			A heap on 4 elements is pictured in the 2nd link, and has breadth first reading word abcd. Then for n = 4 the a(4) = 3 heaps have reading words 1234, 1243, and 1324.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• D. Levin, L. Pudwell, M. Riehl, A. Sandberg, Pattern Avoidance on k-ary Heaps, Slides of Talk, 2014.
• Manda Riehl (joint work with Derek Levin, Lara Pudwell, and Adam Sandberg), Page 92 of the Permutation Patterns 2014 Abstract Book .
• Manda Riehl, A heap on 4 elements

Crossrefs

May be equal to A245899.

Cf. A000108, A056971, A246829.

Formula

a(n) = Sum_{i=0..floor((n-1)/2)} A000108(i)*a(n-i-1) for n > 0.