A173873 a(n) = 2*a(n-1) + 13, a(1)=1.

1, 15, 43, 99, 211, 435, 883, 1779, 3571, 7155, 14323, 28659, 57331, 114675, 229363, 458739, 917491, 1834995, 3670003, 7340019, 14680051, 29360115, 58720243, 117440499, 234881011, 469762035, 939524083, 1879048179, 3758096371

Offset

1,2

Comments

Prime numbers in this sequence are (43, 211, 883, 3571, 14323, 57331, 234881011, 3758096371, 3848290697203, ... )

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = 3*a(n-1) - 2*a(n-2). - Vincenzo Librandi, Jul 15 2012

G.f.: x*(1+12*x)/(1 - 3*x + 2*x^2). - Vincenzo Librandi, Jul 15 2012

a(n) = 7*2^n-13. - Fabio Visonà, Apr 08 2022

Example

a(2) = 2*1  + 13 = 15;
a(3) = 2*15 + 13 = 43;
a(4) = 2*43 + 13 = 99.

Mathematica

RecurrenceTable[{a[1]==1, a[n]==2*a[n-1]+13}, a, {n, 40}] (* Vincenzo Librandi, Jul 15 2012 *)
LinearRecurrence[{3, -2}, {1, 15}, 30] (* Harvey P. Dale, Aug 26 2019 *)

Prog

(Magma) I:=[1]; [n le 1 select I[n] else 2*Self(n-1)+13: n in [1..30]]; // Vincenzo Librandi, Jul 15 2012

Crossrefs

Sequence in context: A072119 A069127 A137183 * A124708 A204734 A126369

Adjacent sequences: A173870 A173871 A173872 * A173874 A173875 A173876

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 06 2010

Status

approved