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)).
n*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-3)*a(n-3) + 2*(2*n-10)*a(n-4) - (n-6)*a(n-6).
MATHEMATICA
CoefficientList[Series[1/Sqrt[1-4 x/(1+x^3)], {x, 0, 40}], x] (* Harvey P. Dale, Feb 06 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-1-2*k, 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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2023
STATUS
approved