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A376696
a(n) = Sum_{k=0..floor(n/3)} binomial(n-3*k,floor(k/3)).
0
1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 6, 8, 10, 12, 15, 18, 21, 24, 28, 33, 39, 47, 57, 69, 84, 102, 123, 147, 175, 208, 247, 294, 351, 420, 504, 606, 729, 876, 1051, 1259, 1506, 1800, 2151, 2571, 3075, 3681, 4410, 5286, 6337, 7596, 9102, 10902, 13053, 15624, 18699, 22380, 26790
OFFSET
0,4
FORMULA
G.f.: (1-x^9)/((1-x^3) * (1-x*(1+x^9))) = (1+x^3+x^6)/(1-x*(1+x^9)).
a(n) = a(n-1) + a(n-10).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n-3*k, k\3));
(PARI) my(N=60, x='x+O('x^N)); Vec((1+x^3+x^6)/(1-x*(1+x^9)))
CROSSREFS
Cf. A376649.
Sequence in context: A104055 A352100 A216200 * A157873 A022870 A237050
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 01 2024
STATUS
approved