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A364017 Expansion of Sum_{k>0} (-1)^(k-1) * x^(3*k-2) / (1 - x^(3*k-2))^3.

%I A364017 #24 Jul 03 2023 01:00:07
%S A364017 1,3,6,9,15,21,29,33,45,54,66,72,92,108,120,125,153,171,191,192,237,
%T A364017 252,276,279,326,354,378,387,435,459,497,489,561,594,645,621,704,744,
%U A364017 786,754,861,924,947,921,1035,1080,1128,1092,1254,1263,1326
%N A364017 Expansion of Sum_{k>0} (-1)^(k-1) * x^(3*k-2) / (1 - x^(3*k-2))^3.
%H A364017 Seiichi Manyama, <a href="/A364017/b364017.txt">Table of n, a(n) for n = 1..10000</a>
%F A364017 G.f.: Sum_{k>0} k*(k+1)/2 * x^k / (1 + x^(3*k)).
%F A364017 a(n) = -Sum_{d|n, n/d==1 (mod 3)} (-1)^(n/d) * binomial(d+1,2).
%t A364017 a[n_] := -DivisorSum[n, (-1)^(n/#) * Binomial[#+1, 2] &, Mod[n/#, 3] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o A364017 (PARI) a(n) = -sumdiv(n, d, (n/d%3==1)*(-1)^(n/d)*binomial(d+1, 2));
%Y A364017 Cf. A364012, A364018.
%K A364017 nonn
%O A364017 1,2
%A A364017 _Seiichi Manyama_, Jul 01 2023