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.

A168610 a(n) = 3^n + 5.

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%I A168610 #26 Sep 08 2022 08:45:49
%S A168610 6,8,14,32,86,248,734,2192,6566,19688,59054,177152,531446,1594328,
%T A168610 4782974,14348912,43046726,129140168,387420494,1162261472,3486784406,
%U A168610 10460353208,31381059614,94143178832,282429536486,847288609448
%N A168610 a(n) = 3^n + 5.
%H A168610 Vincenzo Librandi, <a href="/A168610/b168610.txt">Table of n, a(n) for n = 0..1000</a>
%H A168610 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A168610 a(n) = 3*a(n-1) - 10 with a(0)=6.
%F A168610 G.f.: 2*(3 - 8*x)/((1-x)*(1-3*x)). - _Vincenzo Librandi_, Jul 06 2012
%F A168610 a(n) = 4*a(n-1) -3*a(n-2). - _Vincenzo Librandi_, Jul 06 2012
%F A168610 a(n) = 2*A115098(n)+2. - _Bruno Berselli_, Jul 06 2012
%F A168610 E.g.f.: exp(3*x) + 5*exp(x). - _G. C. Greubel_, Jul 27 2016
%t A168610 CoefficientList[Series[2*(3-8*x)/((1-x)*(1-3*x)),{x,0,40}],x] (* _Vincenzo Librandi_, Jul 06 2012 *)
%t A168610 LinearRecurrence[{4,-3}, {6, 8}, 25] (* _G. C. Greubel_, Jul 27 2016 *)
%o A168610 (Magma) I:=[6, 8]; [n le 2 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jul 06 2012
%o A168610 (PARI) a(n)=3^n+5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A168610 Cf. A168613.
%K A168610 nonn,easy
%O A168610 0,1
%A A168610 _Vincenzo Librandi_, Dec 01 2009
%E A168610 Formula and examples edited to use correct offset by _Jon E. Schoenfield_, Jun 19 2010