A168613 a(n) = 3^n - 5.

-4, -2, 4, 22, 76, 238, 724, 2182, 6556, 19678, 59044, 177142, 531436, 1594318, 4782964, 14348902, 43046716, 129140158, 387420484, 1162261462, 3486784396, 10460353198, 31381059604, 94143178822, 282429536476, 847288609438

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).

Crossrefs

Cf. A168610.

Programs

Magma

I:=[-4, -2]; [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*(7*x-2)/((1-x)*(1-3*x)),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{4,-3}, {-4, -2}, 25] (* G. C. Greubel, Jul 27 2016 *)
3^Range[0,30]-5 (* Harvey P. Dale, Sep 12 2022 *)

Formula

a(n) = 3*a(n-1) + 10 with a(0)=-4.

G.f.: 2*(7*x - 2)/((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*A116970(n) + 2 with A116970(0)=-3, A116970(1)=-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