OFFSET
0,2
LINKS
Winston de Greef, Table of n, a(n) for n = 0..1105
FORMULA
n*a(n) = 3 * ( (3*n-2)*a(n-1) - (3*n-4)*a(n-2) ) for n > 1.
a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-1/3,k) * binomial(k,n-k).
a(n) = A004987(n)*hypergeom([1/2 - n/2, -n/2], [2/3 - n], 4/9). - Peter Luschny, Mar 27 2023
a(n) ~ 3^n * phi^(2*n + 2/3) / (Gamma(1/3) * 5^(1/6) * n^(2/3)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Mar 29 2023
MAPLE
A361843 := n -> (-9)^n*binomial(-1/3, n)*hypergeom([1/2 - n/2, -n/2], [2/3 - n], 4/9): seq(simplify(A361843(n)), n = 0..21); # Peter Luschny, Mar 27 2023
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1-x))^(1/3))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved