OFFSET
0,2
FORMULA
G.f.: 1 / ( sqrt(1-4*x) * (1 - x^3 * c(x)^6) ), where c(x) is the g.f. of A000108.
D-finite with recurrence n*a(n) +2*(-4*n+3)*a(n-1) +8*(2*n-3)*a(n-2) +3*(-n+2)=0. - R. J. Mathar, Mar 12 2023
a(n) = [x^n] 1/(((1-x)^3-x^3) * (1-x)^(n-2)). - Seiichi Manyama, Apr 10 2024
MAPLE
A360168 := proc(n)
add(binomial(2*n, n-3*k), k=0..n/3) ;
end proc:
seq(A360168(n), n=0..70) ; # R. J. Mathar, Mar 12 2023
MATHEMATICA
a[n_] := Sum[Binomial[2*n, 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, n-3*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1-x^3*(2/(1+sqrt(1-4*x)))^6)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 28 2023
STATUS
approved