A353017 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(3*k).

1, 1, 1, 1, 2, 9, 28, 66, 190, 946, 4441, 16650, 67069, 380795, 2220697, 11142307, 58133022, 380165427, 2581541092, 15919859932, 101602799146, 758173118356, 5826902270129, 42158185020684, 316416126945385, 2656178496077301, 22725296418141937, 187568834724460765

Offset: 0

Author

Seiichi Manyama, Apr 16 2022

Keywords

• nonn
• easy

Crossrefs

Cf. A352946, A353015.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[(n-3*k)^(3*k), {k, 0, Floor[n/3]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 16 2022 *)

PARI

a(n) = sum(k=0, n\3, (n-3*k)^(3*k));

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^3)))

Formula

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