A214091 a(n) = 3^n - 2^(n+2).

-3, -5, -7, -5, 17, 115, 473, 1675, 5537, 17635, 54953, 168955, 515057, 1561555, 4717433, 14217835, 42784577, 128615875, 386371913, 1160164315, 3482590097, 10451964595, 31364282393, 94109624395, 282362427617, 847154391715, 2541597392873, 7625060614075, 22875718713137

Offset: 0

Author

Alex Ratushnyak, Jul 03 2012

Keywords

• sign
• easy

Comments

The subsequence of (positive or negative) primes begins: -3, -5, -7, -5, 17, no more through the composite a(116) (which is near 2.2*10^55). - Jonathan Vos Post, Jul 03 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-6).

Crossrefs

Cf. A001047 (3^n - 2^n), A003063 (3^n - 2^(n+1)).

Programs

Magma

[3^n - 2^(n+2): n in [0..30]]; // Vincenzo Librandi, Jun 18 2014

Mathematica

Table[3^n - 2^(n+2), {n, 0, 30}] (* or *) CoefficientList[Series[(-3 + 10 x)/((3 x - 1) (2 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2014 *)

Formula

G.f.: ( -3+10*x ) / ( (3*x-1)*(2*x-1) ). - R. J. Mathar, Jul 07 2012

a(n) = 5*a(n-1) - 6*a(n-2) for n>1. - Vincenzo Librandi, Jun 18 2014