A376649 a(n) = Sum_{k=0..floor(n/3)} binomial(floor(k/3),n-3*k).

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 4, 6, 5, 5, 6, 5, 5, 6, 5, 6, 10, 11, 10, 11, 11, 10, 11, 11, 11, 16, 21, 21, 21, 22, 21, 21, 22, 22, 27, 37, 42, 42, 43, 43, 42, 43, 44, 49, 64, 79, 84, 85, 86, 85, 85, 87, 93, 113, 143

Offset

0,20

Links

Table of n, a(n) for n=0..85.

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

Formula

G.f.: (1-x^9)/((1-x^3) * (1-x^9-x^10)) = (1+x^3+x^6)/(1-x^9-x^10).

a(n) = a(n-9) + a(n-10).

a(n) = A017877(n) + A017877(n-3) + A017877(n-6).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(k\3, n-3*k));
(PARI) my(N=90, x='x+O('x^N)); Vec((1+x^3+x^6)/(1-x^9-x^10))

Crossrefs

Cf. A079398, A376650.

Cf. A017877.

Sequence in context: A161045 A029322 A152828 * A233285 A233284 A112195

Adjacent sequences: A376646 A376647 A376648 * A376650 A376651 A376652

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 01 2024

Status

approved