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