A168611 a(n) = 3^n - 4.

-3, -1, 5, 23, 77, 239, 725, 2183, 6557, 19679, 59045, 177143, 531437, 1594319, 4782965, 14348903, 43046717, 129140159, 387420485, 1162261463, 3486784397, 10460353199, 31381059605, 94143178823, 282429536477, 847288609439

Offset: 0

Author

Vincenzo Librandi, Dec 01 2009

Keywords

• sign
• easy

Links

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

Programs

Magma

I:=[-3, -1]; [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

Table[3^n-4,{n,0,50}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
CoefficientList[Series[(11*x-3)/((1-x)*(1-3*x)),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{4,-3},{-3,-1},30] (* Harvey P. Dale, May 21 2024 *)

Formula

a(n) = 3*a(n-1) + 8 with a(0)=-3.

G.f.: (11*x - 3)/((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

E.g.f.: exp(3*x) - 4*exp(x). - G. C. Greubel, Jul 27 2016

Extensions

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