OFFSET
0,2
FORMULA
G.f.: 1 / ( sqrt(1-4*x) * (1 - x^3) ).
a(n) ~ 2^(2*n + 6) / (63 * sqrt(Pi*n)). - Vaclav Kotesovec, Jan 28 2023
a(n)-a(n-3) = A000984(n). - R. J. Mathar, Mar 12 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
MAPLE
A360153 := proc(n)
add(binomial(2*n-6*k, n-3*k), k=0..n/3) ;
end proc:
seq(A360153(n), n=0..70) ; # R. J. Mathar, Mar 12 2023
MATHEMATICA
a[n_] := Sum[Binomial[2*n - 6*k, n - 3*k], {k, 0, Floor[n/3]}]; Array[a, 26, 0] (* Amiram Eldar, Jan 28 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\3, 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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 28 2023
STATUS
approved