A364067 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(3*k-1)).

0, 1, 0, 3, 0, 4, 0, 5, 2, 6, 0, 7, 0, 13, 0, 9, 0, 10, 6, 11, 0, 15, 0, 20, 0, 14, 0, 15, 8, 23, 0, 17, 0, 27, 0, 19, 0, 28, 10, 21, 4, 22, 0, 34, 0, 33, 0, 25, 12, 26, 0, 36, 0, 51, 0, 29, 0, 30, 14, 31, 0, 43, 10, 48, 0, 39, 0, 35, 16, 48, 0, 37, 0, 66, 0, 39, 0, 53, 18, 52, 0, 42, 0, 62, 12, 58, 0, 45

Offset

1,4

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A359239, A363891.

Cf. A364064, A364065, A364066.

Sequence in context: A297217 A218859 A363028 * A246691 A066705 A277894

Adjacent sequences: A364064 A364065 A364066 * A364068 A364069 A364070

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved