A153079 a(n) = 13^n + 2.

3, 15, 171, 2199, 28563, 371295, 4826811, 62748519, 815730723, 10604499375, 137858491851, 1792160394039, 23298085122483, 302875106592255, 3937376385699291, 51185893014090759, 665416609183179843, 8650415919381337935, 112455406951957393131, 1461920290375446110679

Offset: 0

Author

Vincenzo Librandi, Feb 10 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (14,-13).

Crossrefs

Cf. A141012.

Programs

Magma

I:=[3, 15]; [n le 2 select I[n] else 14*Self(n-1)-13*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 25 2012

Mathematica

LinearRecurrence[{14,-13},{3,15},30]
13^Range[0,20]+2 (* Harvey P. Dale, Aug 13 2019 *)

Formula

From R. J. Mathar, Jan 05 2011: (Start)

a(n) = 1 + A141012(n+1).

G.f.: (3-27*x)/((13*x-1)*(x-1)). (End)

From Elmo R. Oliveira, May 07 2025: (Start)

E.g.f.: (2 + exp(12*x))*exp(x).

a(n) = 14*a(n-1) - 13*a(n-2). (End)

Extensions

a(9) corrected and a(17), a(18) added by R. J. Mathar, Jan 05 2011