A153973 a(n) = 3*a(n-1) - 2*a(n-2), with a(1) = 9, a(2) = 12.

9, 12, 18, 30, 54, 102, 198, 390, 774, 1542, 3078, 6150, 12294, 24582, 49158, 98310, 196614, 393222, 786438, 1572870, 3145734, 6291462, 12582918, 25165830, 50331654, 100663302, 201326598, 402653190, 805306374, 1610612742, 3221225478

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A146529, A153972

Programs

Magma

I:=[9,12]; [n le 2 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Sep 01 2016

Mathematica

a=9;lst={a};Do[a=(a-2)*2-2;AppendTo[lst,a],{n,6!}];lst
NestList[2#-6&,9,30] (* or *) LinearRecurrence[{3,-2},{9,12},31]
Table[ (3/2)*(4 + 2^n), {n, 1, 25}] (* G. C. Greubel, Sep 01 2016 *)

Formula

a(n) = 3*a(n-1) - 2*a(n-2), with a(1) = 9, a(2) = 12. - Harvey P. Dale, May 09 2012

From G. C. Greubel, Sep 01 2016: (Start)

a(n) = (3/2)*(4 + 2^n).

G.f.: 3*x*(3 - 5*x)/((1 - x)*(1 - 2*x)).

E.g.f.: (3/2)*(-5 + 4*exp(x) + exp(2*x)). (End)

Extensions

Definition adapted to offset by Georg Fischer, Jun 18 2021