A363978 Expansion of Sum_{k>0} x^(3*k) / (1 - x^(4*k))^3.

0, 0, 1, 0, 0, 1, 3, 0, 1, 0, 6, 1, 0, 3, 11, 0, 0, 1, 15, 0, 4, 6, 21, 1, 0, 0, 29, 3, 0, 11, 36, 0, 7, 0, 48, 1, 0, 15, 56, 0, 0, 4, 66, 6, 11, 21, 78, 1, 3, 0, 92, 0, 0, 29, 111, 3, 16, 0, 120, 11, 0, 36, 140, 0, 0, 7, 153, 0, 22, 48, 171, 1, 0, 0, 201, 15, 9, 56, 210, 0, 29, 0, 231, 4, 0, 66, 254, 6, 0

Offset: 1

Author

Seiichi Manyama, Jun 30 2023

Keywords

• nonn

Crossrefs

Cf. A363973.

Programs

Mathematica

a[n_] := DivisorSum[n, Binomial[(#+1)/4+1,2] &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

PARI

a(n) = sumdiv(n, d, (d%4==3)*binomial((d+1)/4+1, 2));

Formula

G.f.: Sum_{k>0} k*(k+1)/2 * x^(4*k-1) / (1 - x^(4*k-1)).

a(n) = Sum_{d|n, d==3 mod 4} binomial((d+1)/4+1,2).