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%I #21 Jul 07 2023 06:38:11
%S 0,1,0,3,0,4,0,5,2,6,0,7,0,13,0,9,0,10,6,11,0,15,0,20,0,14,0,15,8,23,
%T 0,17,0,27,0,19,0,28,10,21,4,22,0,34,0,33,0,25,12,26,0,36,0,51,0,29,0,
%U 30,14,31,0,43,10,48,0,39,0,35,16,48,0,37,0,66,0,39,0,53,18,52,0,42,0,62,12,58,0,45
%N Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(3*k-1)).
%H Seiichi Manyama, <a href="/A364067/b364067.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (1/3) * Sum_{d | 3*n-2, d==2 (mod 3)} (d+1).
%F G.f.: Sum_{k>0} x^(2*k) / (1 - x^(3*k-1))^2.
%t a[n_] := DivisorSum[3*n - 2, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *)
%o (PARI) a(n) = sumdiv(3*n-2, d, (d%3==2)*(d+1))/3;
%Y Cf. A359239, A363891.
%Y Cf. A364064, A364065, A364066.
%K nonn
%O 1,4
%A _Seiichi Manyama_, Jul 04 2023
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