A390037 a(n) = Sum_{k=0..floor(n/3)} binomial(k+2,3*n-9*k+2).

1, 0, 0, 3, 0, 0, 6, 0, 0, 10, 1, 0, 15, 6, 0, 21, 21, 0, 28, 56, 1, 36, 126, 9, 45, 252, 45, 55, 462, 165, 67, 792, 495, 90, 1287, 1287, 169, 2002, 3003, 469, 3004, 6435, 1485, 4383, 12870, 4504, 6308, 24310, 12529, 9248, 43759, 31995, 14688, 75600, 75772, 27132

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1,1).

Formula

G.f.: 1 / ((1-x^3)^3 - x^10).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) + a(n-10).

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec(1/((1-x^3)^3-x^10))

Crossrefs

Cf. A390035.

Sequence in context: A194498 A193986 A376203 * A062688 A067181 A390036

Adjacent sequences: A390034 A390035 A390036 * A390038 A390039 A390040

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved