The OEIS is supported by the many generous donors to the OEIS Foundation.

A373452
Number of (binary) heaps of length n whose element set equals [k] (for some k <= n).
4
1, 1, 2, 6, 16, 64, 252, 1460, 6256, 39760, 230056, 1920152, 12154416, 113087888, 916563592, 10586707896, 80444848064, 898922718272, 8634371968224, 117894609062176, 1160052513737280, 16638593775310528, 200744153681516384, 3415784055462112160, 38542918215425934624
OFFSET
0,3
These heaps may contain repeated elements. Their element sets are gap-free and contain 1 (if nonempty).
Eric Weisstein's World of Mathematics, Heap
Wikipedia, Binary heap
EXAMPLE
a(0) = 1: the empty heap.
a(1) = 1: 1.
a(2) = 2: 11, 21.
a(3) = 6: 111, 211, 212, 221, 312, 321.
a(4) = 16: 1111, 2111, 2121, 2211, 2212, 2221, 3121, 3211, 3212, 3221, 3231, 3312, 3321, 4231, 4312, 4321.
(The examples use max-heaps.)
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1,
(g-> (f-> add(b(f, j)*b(n-1-f, j), j=1..k)
)(min(g-1, n-g/2)))(2^ilog2(n)))
end:
a:= n-> add(add(binomial(k, j)*(-1)^j*b(n, k-j), j=0..k), k=0..n):
seq(a(n), n=0..24);
CROSSREFS
Row sums of A373451.
Cf. A000670, A056971 (distinct elements), A373450.
Sequence in context: A173994 A363587 A150032 * A283420 A121749 A009386
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2024
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 10:25 EDT 2024. Contains 376068 sequences. (Running on oeis4.)