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%I #12 Mar 11 2023 14:57:59
%S 1,1,2,4,6,8,12,16,23,27,38,44,60,66,88,96,125,133,170,180,226,236,
%T 292,304,371,383,462,476,568,582,688,704,825,841,978,996,1150,1168,
%U 1340,1360,1551,1571,1782,1804,2036,2058,2312,2336,2613,2637,2938,2964,3290
%N Number of (binary) max-heaps on n elements from the set {0,1} containing exactly three 0's.
%H Alois P. Heinz, <a href="/A326504/b326504.txt">Table of n, a(n) for n = 3..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Heap.html">Heap</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_heap">Binary heap</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,0,0,-2,2,1,-1).
%F 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).
%t 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 *)
%Y Column k=3 of A309049.
%K nonn,easy
%O 3,3
%A _Alois P. Heinz_, Jul 09 2019