OFFSET
0,7
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = 1 - Sum_{k=0..n-4} a(k) * a(n-k-4).
G.f. A(x) satisfies: A(x) = 1/(1-x) - x^4 * A(x)^2.
G.f.: 2 / ( 1-x + sqrt((1-x)^2 + 4*x^4*(1-x)) ).
D-finite with recurrence +(n+4)*a(n) +2*(-n-3)*a(n-1) +(n+2)*a(n-2) +4*(n-2)*a(n-4) +2*(-2*n+5)*a(n-5)=0. - R. J. Mathar, Jan 25 2023
PROG
(PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)*binomial(2*k, k)/(k+1));
(PARI) my(N=50, x='x+O('x^N)); Vec(2/(1-x+sqrt((1-x)^2+4*x^4*(1-x))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 22 2023
STATUS
approved