A083314 (2*4^n-(3^n-1))/2.

1, 3, 12, 51, 216, 903, 3732, 15291, 62256, 252303, 1019052, 4105731, 16511496, 66311703, 266043972, 1066567371, 4273443936, 17115299103, 68525766492, 274296776211, 1097768235576, 4392816334503, 17576495514612, 70321672588251

Offset: 0

Author

Paul Barry, Apr 24 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083313

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-19,12)

Crossrefs

Cf. A083315.

Programs

Mathematica

Table[(2*4^n-(3^n-1))/2,{n,0,30}] (* or *) LinearRecurrence[{8,-19,12},{1,3,12},30] (* Harvey P. Dale, Sep 29 2016 *)

Formula

a(n)=(2*4^n-(3^n-1))/2

G.f. (1-5x+7x^2)/((1-x)(1-3x)(1-4x))

E.g.f. (2exp(4x)-exp(3x)+exp(x))/2