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A376649
a(n) = Sum_{k=0..floor(n/3)} binomial(floor(k/3),n-3*k).
2
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
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. A017877.
Sequence in context: A161045 A029322 A152828 * A233285 A233284 A112195
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 01 2024
STATUS
approved