A168569 a(n) = 9*(3^n - 1)/2.

0, 9, 36, 117, 360, 1089, 3276, 9837, 29520, 88569, 265716, 797157, 2391480, 7174449, 21523356, 64570077, 193710240, 581130729, 1743392196, 5230176597, 15690529800, 47071589409, 141214768236, 423644304717, 1270932914160

Offset: 0

Author

Vincenzo Librandi, Nov 30 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A003462.

Programs

Magma

[9*(3^n-1)/2: n in [0..30]]; // Vincenzo Librandi, Sep 24 2014

Mathematica

9 (3^Range[0,30]-1)/2  (* Harvey P. Dale, Mar 18 2011 *)
CoefficientList[Series[9 x / ((1 - x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 24 2014 *)

PARI

a(n)=9*(3^n-1)/2 \\ Charles R Greathouse IV, Jul 26 2016

Formula

From R. J. Mathar, Jan 04 2011: (Start)

a(n) = 9*A003462(n).

G.f.: 9*x / ( (3*x-1)*(x-1) ). (End)

a(n) = 4*a(n-1)-3*a(n-2). - Robert Israel, Sep 24 2014

E.g.f.: (9/2)*(exp(3*x) - exp(x)). - G. C. Greubel, Jul 26 2016