A363029 Expansion of Sum_{k>0} k * x^(4*k-2) / (1 - x^(5*k-3)).

0, 1, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 2, 5, 0, 1, 0, 6, 0, 3, 0, 10, 0, 1, 0, 8, 2, 1, 0, 9, 4, 1, 0, 15, 0, 1, 0, 11, 0, 6, 2, 12, 0, 1, 0, 16, 0, 7, 6, 14, 0, 1, 0, 15, 2, 1, 0, 26, 0, 1, 0, 24, 0, 1, 4, 18, 8, 1, 2, 22, 0, 1, 0, 20, 0, 18, 0, 21, 0, 1, 0, 29, 2, 6, 10, 23, 0, 1, 0, 33, 0, 1, 0

Offset

1,6

Links

Table of n, a(n) for n=1..93.

Formula

a(n) = (1/5) * Sum_{d | 5*n-2, d==2 (mod 5)} (d+3).

G.f.: Sum_{k>0} x^(2*k) / (1 - x^(5*k-1))^2.

Mathematica

a[n_] := DivisorSum[5*n - 2, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-2, d, (d%5==2)*(d+3))/5;

Crossrefs

Cf. A359269, A363025.

Sequence in context: A284148 A108197 A318455 * A049769 A117179 A111526

Adjacent sequences: A363026 A363027 A363028 * A363030 A363031 A363032

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2023

Status

approved