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%I #21 Sep 08 2022 08:45:50
%S 1,15,43,99,211,435,883,1779,3571,7155,14323,28659,57331,114675,
%T 229363,458739,917491,1834995,3670003,7340019,14680051,29360115,
%U 58720243,117440499,234881011,469762035,939524083,1879048179,3758096371
%N a(n) = 2*a(n-1) + 13, a(1)=1.
%C Prime numbers in this sequence are (43, 211, 883, 3571, 14323, 57331, 234881011, 3758096371, 3848290697203, ... )
%H Vincenzo Librandi, <a href="/A173873/b173873.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = 3*a(n-1) - 2*a(n-2). - _Vincenzo Librandi_, Jul 15 2012
%F G.f.: x*(1+12*x)/(1 - 3*x + 2*x^2). - _Vincenzo Librandi_, Jul 15 2012
%F a(n) = 7*2^n-13. - _Fabio Visonà_, Apr 08 2022
%e a(2) = 2*1 + 13 = 15;
%e a(3) = 2*15 + 13 = 43;
%e a(4) = 2*43 + 13 = 99.
%t RecurrenceTable[{a[1]==1,a[n]==2*a[n-1]+13},a,{n,40}] (* _Vincenzo Librandi_, Jul 15 2012 *)
%t LinearRecurrence[{3,-2},{1,15},30] (* _Harvey P. Dale_, Aug 26 2019 *)
%o (Magma) I:=[1]; [n le 1 select I[n] else 2*Self(n-1)+13: n in [1..30]]; // _Vincenzo Librandi_, Jul 15 2012
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, Mar 06 2010