A135583 a(n) = 4*a(n-1) - 4 for n>0, a(0)=3.

3, 8, 28, 108, 428, 1708, 6828, 27308, 109228, 436908, 1747628, 6990508, 27962028, 111848108, 447392428, 1789569708, 7158278828, 28633115308, 114532461228, 458129844908, 1832519379628, 7330077518508, 29320310074028

Offset: 0

Author

Paul Curtz, Feb 25 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A003947.

Programs

Magma

[(4+5*4^n)/3: n in [0..30]]; // Vincenzo Librandi, Aug 10 2011

Mathematica

NestList[4#-4&,3,30] (* or *) LinearRecurrence[{5,-4},{3,8},30] (* Harvey P. Dale, Feb 27 2013 *)

Formula

From R. J. Mathar, Mar 31 2008: (Start)

a(n) = (4 + 5*4^n)/3.

a(n) - a(n-1) = A003947(n).

O.g.f.: (3 - 7*x)/((1 - x)*(1 - 4*x)). (End)

a(0)=3, a(1)=8; for n>1, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Feb 27 2013

E.g.f.: (1/3)*(4*exp(x) + 5*exp(4*x)). - G. C. Greubel, Oct 20 2016

Extensions

More terms from R. J. Mathar, Mar 31 2008