A364064 Expansion of Sum_{k>0} k * x^k / (1 - x^(3*k-2)).

1, 3, 4, 5, 6, 9, 8, 9, 10, 16, 12, 13, 14, 21, 16, 17, 21, 26, 20, 21, 22, 31, 24, 32, 26, 36, 28, 29, 30, 41, 40, 33, 34, 50, 36, 37, 38, 60, 40, 41, 42, 56, 44, 54, 56, 61, 48, 49, 50, 66, 52, 64, 54, 81, 56, 57, 63, 76, 72, 61, 62, 81, 64, 76, 66, 99, 68, 69, 70, 102, 72, 73, 88, 108, 76, 77, 78, 101

Offset

1,2

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A359212, A363889.

Sequence in context: A277898 A212640 A333694 * A338321 A220844 A047250

Adjacent sequences: A364061 A364062 A364063 * A364065 A364066 A364067

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved