%I #10 May 10 2018 09:41:45
%S 1,1,1,1,2,2,2,3,4,5,4,6,8,9,10,11,14,16,18,21,25,28,31,36,41,48,52,
%T 59,69,77,85,96,109,121,133,151,172,189,208,231,260,287,316,350,390,
%U 432,471,521,578,636,695,764,842,924,1009,1107,1218,1330,1449,1584
%N Expansion of Product_{k>=1} (1 + x^k - x^(3*k)).
%H Vaclav Kotesovec, <a href="/A266686/b266686.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2*sqrt(Pi)*n^(3/4)), where c = Integral_{0..infinity} log(1 + exp(-x) - exp(-3*x)) dx = 0.59698046904738615106237970379036510874974380079287087827737... . - _Vaclav Kotesovec_, Jan 05 2016
%t nmax=60; CoefficientList[Series[Product[1+x^k-x^(3*k), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 100; p = ConstantArray[0, nmax + 1]; p[[1]] = 1; p[[2]] = 1; p[[4]] = -1; Do[Do[p[[j+1]] = p[[j+1]] + p[[j - k + 1]] - If[j < 3*k, 0, p[[j - 3*k + 1]]], {j, nmax, k, -1}];, {k, 2, nmax}]; p (* _Vaclav Kotesovec_, May 10 2018 *)
%Y Cf. A264905, A266647, A266650, A275820.
%K nonn
%O 0,5
%A _Vaclav Kotesovec_, Jan 02 2016