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%I #13 Jul 01 2023 09:25:40
%S 1,4,9,15,25,36,50,60,81,99,121,135,170,200,225,239,289,324,362,371,
%T 450,483,529,540,626,680,729,750,841,891,962,956,1089,1155,1250,1215,
%U 1370,1448,1530,1483,1681,1800,1850,1811,2025,2115,2209,2151,2451,2479,2601,2550,2809,2916,3026
%N Expansion of Sum_{k>0} k^2 * x^k / (1 + x^(3*k)).
%F a(n) = -Sum_{d|n, n/d==1 (mod 3)} (-1)^(n/d) * d^2.
%t a[n_] := -DivisorSum[n, (-1)^(n/#) * #^2 &, Mod[n/#, 3] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 01 2023 *)
%o (PARI) a(n) = -sumdiv(n, d, (n/d%3==1)*(-1)^(n/d)*d^2);
%Y Cf. A364011, A364012.
%Y Cf. A050470.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jul 01 2023
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