A364084 Expansion of Sum_{k>0} k * x^(3*k) / (1 - x^(4*k-1)).

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, 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, 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

Offset: 1

Author

Seiichi Manyama, Jul 04 2023

Keywords

• nonn

Crossrefs

Cf. A359240.

Programs

Mathematica

a[n_] := DivisorSum[4*n - 3, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)

PARI

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

Formula

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

G.f.: Sum_{k>0} x^(3*k) / (1 - x^(4*k-1))^2.