A367042 G.f. satisfies A(x) = 1 + x^3 + x*A(x)^2.

1, 1, 2, 6, 16, 48, 152, 500, 1688, 5816, 20368, 72288, 259424, 939808, 3432192, 12622416, 46706144, 173762016, 649569216, 2438748864, 9191656192, 34765298944, 131912452864, 501987944832, 1915417307392, 7326620001536, 28088736525824, 107913607531520

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: A(x) = 2*(1+x^3) / (1+sqrt(1-4*x*(1+x^3))).

a(n) = Sum_{k=0..floor(n/3)} binomial(n-3*k+1,k) * binomial(2*(n-3*k),n-3*k)/(n-3*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n-3*k+1, k)*binomial(2*(n-3*k), n-3*k)/(n-3*k+1));

Crossrefs

Cf. A366676, A367043.

Cf. A025227, A176697.

Cf. A226022.

Sequence in context: A360856 A046721 A230929 * A291189 A214843 A272411

Adjacent sequences: A367039 A367040 A367041 * A367043 A367044 A367045

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2023

Status

approved