A360186 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-6*k,n-3*k).

1, 2, 6, 19, 68, 246, 905, 3364, 12624, 47715, 181392, 692808, 2656441, 10219208, 39423792, 152461079, 590861182, 2294182428, 8922674221, 34754402618, 135552346392, 529335200219, 2069344561102, 8097878381208, 31718268482881, 124341261876650

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1 / ( sqrt(1-4*x) * (1 + x^3) ).

a(n) ~ 2^(2*n + 6) / (65*sqrt(Pi*n)). - Vaclav Kotesovec, Jan 29 2023

D-finite with recurrence n*a(n) +2*(-2*n+1)*a(n-1) +n*a(n-3) +2*(-2*n+1)*a(n-4)=0. - R. J. Mathar, Mar 12 2023

a(n)+a(n-3) = A000984(n). - R. J. Mathar, Mar 12 2023

Maple

A360186 := proc(n)
    add((-1)^k*binomial(2*n-6*k, n-3*k), k=0..n/3) ;
end proc:
seq(A360186(n), n=0..70) ; # R. J. Mathar, Mar 12 2023

Mathematica

Table[Sum[(-1)^k Binomial[2n-6k, n-3k], {k, 0, Floor[n/3]}], {n, 0, 30}] (* Harvey P. Dale, Mar 05 2023 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-6*k, n-3*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+x^3)))

Crossrefs

Cf. A054108, A360185.

Cf. A000984, A360153.

Sequence in context: A148471 A007721 A150099 * A150100 A150101 A150102

Adjacent sequences: A360183 A360184 A360185 * A360187 A360188 A360189

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 29 2023

Status

approved