A168610 a(n) = 3^n + 5.

6, 8, 14, 32, 86, 248, 734, 2192, 6566, 19688, 59054, 177152, 531446, 1594328, 4782974, 14348912, 43046726, 129140168, 387420494, 1162261472, 3486784406, 10460353208, 31381059614, 94143178832, 282429536486, 847288609448

Offset: 0

Author

Vincenzo Librandi, Dec 01 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. A168613.

Programs

Magma

I:=[6, 8]; [n le 2 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jul 06 2012

Mathematica

CoefficientList[Series[2*(3-8*x)/((1-x)*(1-3*x)),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{4,-3}, {6, 8}, 25] (* G. C. Greubel, Jul 27 2016 *)

PARI

a(n)=3^n+5 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3*a(n-1) - 10 with a(0)=6.

G.f.: 2*(3 - 8*x)/((1-x)*(1-3*x)). - Vincenzo Librandi, Jul 06 2012

a(n) = 4*a(n-1) -3*a(n-2). - Vincenzo Librandi, Jul 06 2012

a(n) = 2*A115098(n)+2. - Bruno Berselli, Jul 06 2012

E.g.f.: exp(3*x) + 5*exp(x). - G. C. Greubel, Jul 27 2016

Extensions

Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010