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%I #12 Jul 05 2023 01:44:57
%S 0,0,1,0,0,3,0,0,4,0,0,5,2,0,6,0,0,7,0,5,8,0,0,9,0,0,16,0,0,11,3,0,12,
%T 7,0,13,0,0,14,0,8,22,0,0,16,0,0,26,0,0,18,0,8,19,10,0,24,0,0,21,0,11,
%U 22,9,0,23,0,0,36,0,0,34,0,0,36,13,0,27,0,0,28,0,14,29,0,11,40,0,0,46,5,0,32,0,0
%N Expansion of Sum_{k>0} k * x^(3*k) / (1 - x^(4*k-1)).
%F a(n) = (1/4) * Sum_{d | 4*n-3, d==3 (mod 4)} (d+1).
%F G.f.: Sum_{k>0} x^(3*k) / (1 - x^(4*k-1))^2.
%t a[n_] := DivisorSum[4*n - 3, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *)
%o (PARI) a(n) = sumdiv(4*n-3, d, (d%4==3)*(d+1))/4;
%Y Cf. A359240.
%K nonn
%O 1,6
%A _Seiichi Manyama_, Jul 04 2023
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