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

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4).

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A199210.

Sequence in context: A015237 A024223 A251720 * A331764 A372500 A249923

Adjacent sequences: A199208 A199209 A199210 * A199212 A199213 A199214

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 04 2011

Status

approved