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%I #13 Apr 14 2022 02:40:51
%S 1,0,0,1,1,1,2,9,65,514,4124,33498,281829,2628658,31130220,521900363,
%T 11550872369,292093228523,7763038391586,210839178560483,
%U 5844964107402065,168148032885913260,5206234971937519704,183267822341124743772,7684147885975909244473
%N a(n) = Sum_{k=0..floor(n/3)} k^(3*(n-3*k)).
%F G.f.: Sum_{k>=0} x^(3 * k) / (1 - k^3 * x).
%F a(n) ~ sqrt(2*Pi) * (n/(3*LambertW(exp(1)*n/3)))^(3*n + 1/2 - 3*n/LambertW(exp(1)*n/3)) / (3*sqrt(1 + LambertW(exp(1)*n/3))). - _Vaclav Kotesovec_, Apr 14 2022
%t a[0] = 1; a[n_] := Sum[k^(3*(n - 3*k)), {k, 0, Floor[n/3]}]; Array[a, 25, 0] (* _Amiram Eldar_, Apr 13 2022 *)
%o (PARI) a(n) = sum(k=0, n\3, k^(3*(n-3*k)));
%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/(1-k^3*x)))
%Y Cf. A352945.
%K nonn,easy
%O 0,7
%A _Seiichi Manyama_, Apr 13 2022
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