A168616 - OEIS

%I #37 Sep 08 2022 08:45:49

%S -4,-3,-1,3,11,27,59,123,251,507,1019,2043,4091,8187,16379,32763,

%T 65531,131067,262139,524283,1048571,2097147,4194299,8388603,16777211,

%U 33554427,67108859,134217723,268435451,536870907,1073741819,2147483643

%N a(n) = 2^n - 5.

%H Vincenzo Librandi, <a href="/A168616/b168616.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature(3,-2).

%F a(n) = 2*a(n-1) + 5.

%F G.f. (9*x - 4)/((x-1)*(2*x-1)). - _R. J. Mathar_, Feb 22 2012

%F a(n) = 3*a(n-1) - 2*a(n-2). - _Vincenzo Librandi_, Sep 19 2013

%F E.g.f.: exp(2*x) - 5*exp(x). - _G. C. Greubel_, Jul 27 2016

%t Table[2^n-5,{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 22 2010 *)

%t CoefficientList[Series[(9 x - 4)/((x - 1) (2 x - 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)

%t LinearRecurrence[{3,-2},{-4,-3},40] (* _Harvey P. Dale_, Oct 15 2014 *)

%o (Magma) [2^n-5: n in [0..40]]; // _Vincenzo Librandi_, Sep 19 2013

%o (PARI) a(n)=2^n-5 \\ _Charles R Greathouse IV_, Oct 07 2015

%K sign,easy

%O 0,1

%A _Vincenzo Librandi_, Dec 01 2009

%E Formula and examples edited to use correct offset by _Jon E. Schoenfield_, Jun 19 2010