A371842 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k+1,n-3*k).

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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)

Mathematica

Table[Sum[Binomial[2n-2k+1, n-3k], {k, 0, Floor[n/3]}], {n, 0, 30}] (* Harvey P. Dale, Oct 26 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*n-2*k+1, n-3*k));

Crossrefs

Cf. A105872.

Sequence in context: A329533 A390702 A102871 * A277287 A119374 A371773

Adjacent sequences: A371839 A371840 A371841 * A371843 A371844 A371845

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2024

Status

approved