A363032 Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-3)).

0, 1, 0, 1, 2, 1, 0, 4, 0, 1, 4, 3, 0, 6, 0, 1, 6, 1, 2, 11, 0, 1, 8, 1, 0, 12, 0, 5, 10, 1, 0, 15, 2, 1, 12, 6, 0, 14, 0, 3, 14, 1, 0, 25, 4, 1, 18, 1, 0, 18, 0, 8, 18, 3, 0, 23, 0, 6, 20, 9, 2, 26, 0, 1, 22, 1, 0, 38, 0, 1, 30, 1, 0, 26, 2, 11, 26, 1, 4, 36, 0, 3, 28, 19, 0, 30, 0, 1, 32, 1, 0, 47, 0

Offset

1,5

Links

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

Formula

a(n) = (1/5) * Sum_{d | 5*n-4, d==2 (mod 5)} (d+3).

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

Mathematica

a[n_] := DivisorSum[5*n - 4, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-4, d, (d%5==2)*(d+3))/5;

Crossrefs

Cf. A359244, A363027.

Sequence in context: A300482 A191897 A088850 * A185964 A143424 A130125

Adjacent sequences: A363029 A363030 A363031 * A363033 A363034 A363035

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2023

Status

approved