A168609 a(n) = 3^n + 4.

5, 7, 13, 31, 85, 247, 733, 2191, 6565, 19687, 59053, 177151, 531445, 1594327, 4782973, 14348911, 43046725, 129140167, 387420493, 1162261471, 3486784405, 10460353207, 31381059613, 94143178831, 282429536485, 847288609447

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-3).

Formula

a(n) = 3*a(n-1) - 8, with n>0, a(0)=5.

G.f.: (5 - 13*x)/((1-x)*(1-3 x)). - Vincenzo Librandi, May 13 2014

a(n) = 4*a(n-1) - 3*a(n-2) for n>1. - Vincenzo Librandi, May 13 2014

E.g.f.: exp(3*x) + 4*exp(x). - G. C. Greubel, Jul 27 2016

Example

a(1)=3*5-8=7; a(2)=3*7-8=13; a(3)=3*13-8=31.

Mathematica

Table[3^n + 4, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
CoefficientList[Series[(5 - 13 x)/((1 - x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)
LinearRecurrence[{4, -3}, {5, 7}, 30] (* Harvey P. Dale, Mar 11 2023 *)

Prog

(Magma) [3^n+4: n in [0..30]]; // Vincenzo Librandi, May 13 2014

Crossrefs

Cf. A034472, A168607, A168610, A178674.

Sequence in context: A141191 A101782 A288889 * A266951 A102903 A294064

Adjacent sequences: A168606 A168607 A168608 * A168610 A168611 A168612

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 01 2009

Extensions

Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010

Status

approved