A363977 Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^3.
1, 1, 1, 1, 4, 1, 1, 1, 7, 4, 1, 1, 11, 1, 4, 1, 16, 7, 1, 4, 22, 1, 1, 1, 32, 11, 7, 1, 37, 4, 1, 1, 46, 16, 4, 7, 56, 1, 11, 4, 67, 22, 1, 1, 88, 1, 1, 1, 92, 32, 16, 11, 106, 7, 4, 1, 121, 37, 1, 4, 137, 1, 28, 1, 167, 46, 1, 16, 172, 4, 1, 7, 191, 56, 32, 1, 211, 11, 1, 4, 238, 67, 1
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, Binomial[(#+3)/4+1,2] &, Mod[#, 4] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)
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PARI
a(n) = sumdiv(n, d, (d%4==1)*binomial((d+3)/4+1, 2));
Formula
G.f.: Sum_{k>0} k*(k+1)/2 * x^(4*k-3) / (1 - x^(4*k-3)).
a(n) = Sum_{d|n, d==1 mod 4} binomial((d+3)/4+1,2).