A202206 a(n) = 3*a(n-1)+3*a(n-2) with a(0)=1 and a(1)=2.

1, 2, 9, 33, 126, 477, 1809, 6858, 26001, 98577, 373734, 1416933, 5372001, 20366802, 77216409, 292749633, 1109898126, 4207943277, 15953524209, 60484402458, 229313780001, 869394547377, 3296124982134

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (3,3).

Formula

G.f.: (1-x)/(1-3*x-3*x^2).

a(n) = 1/2*((3/2+1/2*sqrt(21))^n+(3/2-1/2*sqrt(21))^n)+1/42*sqrt(21)*((3/2+1/2*sqrt(21))^n-(3/2-1 /2*sqrt(21))^n). - Paolo P. Lava, Jan 31 2012.

Mathematica

LinearRecurrence[{3, 3}, {1, 2}, 30] (* Harvey P. Dale, Aug 03 2020 *)

Prog

(PARI) Vec((1-x)/(1-3*x-3*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 31 2012

Crossrefs

Cf. A104934, A112117.

Sequence in context: A048498 A215695 A289600 * A150921 A150922 A150923

Adjacent sequences: A202203 A202204 A202205 * A202207 A202208 A202209

Keyword

nonn,easy

Author

Philippe Deléham, Dec 14 2011

Status

approved