OFFSET
0,3
FORMULA
G.f.: c(x * (1-x^3)), where c(x) is the g.f. of A000108.
a(n) ~ 2 * sqrt(1-3*r) / (sqrt(Pi) * n^(3/2) * r^n), where r = 0.2541737124933... is the smallest positive root of the equation 1 - 4*r + 4*r^4 = 0. - Vaclav Kotesovec, Feb 01 2023
D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(-n-1)*a(n-3) +2*(4*n-11)*a(n-4) +4*(-n+5)*a(n-7)=0. - R. J. Mathar, Mar 12 2023
MAPLE
A360271 := proc(n)
add((-1)^k*binomial(n-3*k, k)*A000108(n-3*k), k=0..n/3) ;
end proc:
seq(A360271(n), n=0..70) ; # R. J. Mathar, Mar 12 2023
PROG
(PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)*binomial(2*(n-3*k), n-3*k)/(n-3*k+1));
(PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+(sqrt(1-4*x*(1-x^3)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 31 2023
STATUS
approved