cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A168611 a(n) = 3^n - 4.

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%I A168611 #25 May 21 2024 15:14:36
%S A168611 -3,-1,5,23,77,239,725,2183,6557,19679,59045,177143,531437,1594319,
%T A168611 4782965,14348903,43046717,129140159,387420485,1162261463,3486784397,
%U A168611 10460353199,31381059605,94143178823,282429536477,847288609439
%N A168611 a(n) = 3^n - 4.
%H A168611 Vincenzo Librandi, <a href="/A168611/b168611.txt">Table of n, a(n) for n = 0..1000</a>
%H A168611 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A168611 a(n) = 3*a(n-1) + 8 with a(0)=-3.
%F A168611 G.f.: (11*x - 3)/((1-x)*(1-3*x)). - _Vincenzo Librandi_, Jul 06 2012
%F A168611 a(n) = 4*a(n-1) - 3*a(n-2). - _Vincenzo Librandi_, Jul 06 2012
%F A168611 E.g.f.: exp(3*x) - 4*exp(x). - _G. C. Greubel_, Jul 27 2016
%t A168611 Table[3^n-4,{n,0,50}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%t A168611 CoefficientList[Series[(11*x-3)/((1-x)*(1-3*x)),{x,0,40}],x] (* _Vincenzo Librandi_, Jul 06 2012 *)
%t A168611 LinearRecurrence[{4,-3},{-3,-1},30] (* _Harvey P. Dale_, May 21 2024 *)
%o A168611 (Magma) I:=[-3, -1]; [n le 2 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jul 06 2012
%K A168611 sign,easy
%O A168611 0,1
%A A168611 _Vincenzo Librandi_, Dec 01 2009
%E A168611 Formula and examples edited to use correct offset by _Jon E. Schoenfield_, Jun 19 2010