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
Examples
a(1)=3*5-8=7; a(2)=3*7-8=13; a(3)=3*13-8=31.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-3).
Programs
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Magma
[3^n+4: n in [0..30]]; // Vincenzo Librandi, May 13 2014
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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 *)
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
Extensions
Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010