OFFSET
0,2
FORMULA
a(n) = [x^n] 1/(((1-x)^3-x^3) * (1-x)^n).
a(n) = binomial(2*(n+1), n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [1+n/3, (4+n)/3, (5+n)/3], -1). - Stefano Spezia, Apr 06 2024
From Vaclav Kotesovec, Apr 08 2024: (Start)
Recurrence: n*a(n) = 3*(3*n-2)*a(n-1) - 6*(4*n-5)*a(n-2) + 8*(2*n-3)*a(n-3).
G.f.: (1 + sqrt(1-4*x))/(2*(1-x)*(1-4*x)).
a(n) ~ 2^(2*n+1)/3. (End)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*n+2, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 05 2024
STATUS
approved