OFFSET
0,4
LINKS
Winston de Greef, Table of n, a(n) for n = 0..3162
FORMULA
G.f.: 1/sqrt(1 - 4 * x^3 * (1+x)^2).
a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,k) * binomial(2*k,n-3*k).
From Vaclav Kotesovec, Mar 22 2023: (Start)
Recurrence: n*a(n) = 2*(2*n-3)*a(n-3) + 8*(n-2)*a(n-4) + 2*(2*n-5)*a(n-5).
a(n) ~ 1 / (sqrt((5 - 8*r^3 - 8*r^4)*Pi*n) * r^n), where r = 0.484163615233802299545617907511361266999078019358842974840776720... is the real root of the equation -1 + 4*r^3 + 8*r^4 + 4*r^5 = 0. (End)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*k, k)*binomial(2*k, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 22 2023
STATUS
approved