A199211 a(n) = 11*4^n + 1.

12, 45, 177, 705, 2817, 11265, 45057, 180225, 720897, 2883585, 11534337, 46137345, 184549377, 738197505, 2952790017, 11811160065, 47244640257, 188978561025, 755914244097, 3023656976385, 12094627905537, 48378511622145, 193514046488577, 774056185954305, 3096224743817217

Offset: 0

Author

Vincenzo Librandi, Nov 04 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A199210.

Programs

Magma

[11*4^n+1: n in [0..30]];

Mathematica

11*4^Range[0,30]+1 (* or *) LinearRecurrence[{5,-4},{12,45},30] (* Harvey P. Dale, Oct 10 2012 *)

Formula

a(n) = 4*a(n-1) - 3.

a(n) = 5*a(n-1) - 4*a(n-2).

G.f.: 3*(4-5*x)/((1-x)*(1-4*x)). - Bruno Berselli, Nov 04 2011

From Elmo R. Oliveira, Mar 06 2025: (Start)

E.g.f.: exp(x)*(1 + 11*exp(3*x)).

a(n) = 3*A199210(n). (End)