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A371842
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k+1,n-3*k).
2
1, 3, 10, 36, 133, 498, 1882, 7161, 27391, 105210, 405499, 1567332, 6072724, 23578221, 91712089, 357301827, 1393986898, 5445422340, 21296030401, 83370591273, 326688422203, 1281227165640, 5028742763407, 19751799462378, 77632592859316, 305316702610581
OFFSET
0,2
FORMULA
a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(n+1)).
From Vaclav Kotesovec, Apr 08 2024: (Start)
Recurrence: (n-1)*a(n) = (9*n-11)*a(n-1) - 2*(11*n-16)*a(n-2) + (9*n-13)*a(n-3) - 2*(2*n-3)*a(n-4).
G.f.: 2 / (4*x^2 + 3*x*sqrt(1-4*x) - 9*x + 2).
a(n) ~ 2^(2*n+3) / (3*sqrt(Pi*n)). (End)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*n-2*k+1, n-3*k));
CROSSREFS
Cf. A105872.
Sequence in context: A055989 A329533 A102871 * A277287 A119374 A371773
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 08 2024
STATUS
approved