A364065 Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(3*k-2)).

1, 1, 3, 1, 4, 1, 7, 1, 6, 1, 9, 4, 8, 1, 11, 1, 14, 1, 16, 1, 12, 6, 15, 1, 14, 4, 27, 1, 16, 1, 19, 8, 21, 1, 26, 1, 32, 1, 23, 4, 22, 10, 31, 1, 24, 1, 44, 6, 26, 1, 36, 12, 28, 4, 31, 1, 46, 1, 47, 1, 40, 14, 35, 1, 34, 1, 64, 4, 36, 8, 39, 16, 38, 6, 60, 1, 60, 1, 43, 1, 50, 21, 56, 1, 44, 1, 74, 1, 56, 1

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

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

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

Mathematica

a[n_] := DivisorSum[3*n - 1, # + 2 &, Mod[#, 3] == 1 &]/3; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)

Prog

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

Crossrefs

Cf. A359211, A363514.

Sequence in context: A180251 A094119 A210622 * A335113 A295276 A301856

Adjacent sequences: A364062 A364063 A364064 * A364066 A364067 A364068

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved