OFFSET
0,2
FORMULA
a(n) = [x^n] 1/(((1-x)^3+x^3) * (1-x)^n).
a(n) = binomial(2*(1+n), n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [1+n/3, (4+n)/3, (5+n)/3], 1). - Stefano Spezia, Apr 07 2024
a(n) ~ 2^(2*n+1) / sqrt(Pi*n). - Vaclav Kotesovec, Apr 19 2024
PROG
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n+2, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 06 2024
STATUS
approved