OFFSET
2,2
LINKS
FORMULA
a(n) = binomial(3n-3, n-2) - 2*binomial(3n-6, n-3).
G.f.: (2*g^3-4*g^2+2*g-1)/((1-3*g)*(g-1)^3) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011
D-finite with recurrence +2*(2*n-1)*(n-2)*a(n) +(-43*n^2+169*n-160)*a(n-1) +4*(31*n^2-196*n+292)*a(n-2) -12*(3*n-13)*(3*n-14)*a(n-3)=0. - R. J. Mathar, Jul 26 2022
PROG
(PARI) a(n) = binomial(3*n-3, n-2) - 2*binomial(3*n-6, n-3); \\ Andrew Howroyd, Nov 12 2017
(PARI) \\ here b(n) is x^2 * g.f. of A006013.
b(n)={serreverse(x-2*x^2+x^3 + O(x^n))}
s(n)={(g->(2*g^3-4*g^2+2*g-1)/((1-3*g)*(g-1)^3))(b(n)) + O(x^n)}
Vec(s(25)) \\ Andrew Howroyd, Nov 12 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved