A326504 Number of (binary) max-heaps on n elements from the set {0,1} containing exactly three 0's.

1, 1, 2, 4, 6, 8, 12, 16, 23, 27, 38, 44, 60, 66, 88, 96, 125, 133, 170, 180, 226, 236, 292, 304, 371, 383, 462, 476, 568, 582, 688, 704, 825, 841, 978, 996, 1150, 1168, 1340, 1360, 1551, 1571, 1782, 1804, 2036, 2058, 2312, 2336, 2613, 2637, 2938, 2964, 3290

Offset: 3

Author

Alois P. Heinz, Jul 09 2019

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..10000
• Eric Weisstein's World of Mathematics, Heap
• Wikipedia, Binary heap
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,0,0,-2,2,1,-1).

Crossrefs

Column k=3 of A309049.

Programs

Mathematica

LinearRecurrence[{1,2,-2,0,0,-2,2,1,-1},{1,1,2,4,6,8,12,16,23},60] (* Harvey P. Dale, Mar 11 2023 *)

Formula

G.f.: x^3*(2*x^6-2*x^5+2*x^3-x^2+1)/((x^2+1)*(x+1)^3*(x-1)^4).