A364085 Expansion of Sum_{k>0} k * x^k / (1 - x^(4*k-1)).

1, 2, 3, 5, 5, 6, 8, 8, 11, 11, 11, 12, 14, 17, 15, 19, 17, 18, 24, 20, 21, 23, 25, 29, 29, 26, 27, 29, 35, 32, 32, 32, 33, 46, 35, 39, 40, 38, 47, 41, 41, 42, 49, 55, 45, 47, 50, 48, 64, 50, 53, 59, 53, 65, 56, 56, 57, 64, 71, 60, 69, 67, 63, 82, 67, 66, 68, 68, 86, 79, 71, 74, 74, 89, 81, 77, 77, 78

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A364063, A364066.

Cf. A078703.

Sequence in context: A066113 A363156 A214881 * A163831 A326399 A192419

Adjacent sequences: A364082 A364083 A364084 * A364086 A364087 A364088

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved