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.

A168273 a(n) = 2*n + (-1)^n - 1.

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%I A168273 #23 Sep 08 2022 08:45:48
%S A168273 0,4,4,8,8,12,12,16,16,20,20,24,24,28,28,32,32,36,36,40,40,44,44,48,
%T A168273 48,52,52,56,56,60,60,64,64,68,68,72,72,76,76,80,80,84,84,88,88,92,92,
%U A168273 96,96,100,100,104,104,108,108,112,112,116,116,120,120,124,124,128,128,132
%N A168273 a(n) = 2*n + (-1)^n - 1.
%H A168273 Vincenzo Librandi, <a href="/A168273/b168273.txt">Table of n, a(n) for n = 1..1000</a>
%H A168273 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A168273 From  _R. J. Mathar_, Jan 05 2011: (Start)
%F A168273 G.f.: 4*x^2/( (1+x)*(1-x)^2).
%F A168273 a(n) = 2*A052928(n).
%F A168273 a(n) = A008586(floor(n/2)). (End)
%F A168273 a(n) = 2*n - 2*(n mod 2). - _Wesley Ivan Hurt_, Jun 30 2013
%F A168273 E.g.f.: (1 + (2*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 16 2016
%t A168273 CoefficientList[Series[4 x / ((1+x) (1-x)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, May 14 2013 *)
%t A168273 LinearRecurrence[{1,1,-1},{0,4,4},50] (* _G. C. Greubel_, Jul 16 2016 *)
%o A168273 (Magma) [2*n-1 + (-1)^n: n in [1..70]] // _Vincenzo Librandi_, May 14 2013
%o A168273 (PARI) a(n)=2*n-1+(-1)^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A168273 Cf. A052928, A008586.
%K A168273 nonn,easy
%O A168273 1,2
%A A168273 _Vincenzo Librandi_, Nov 22 2009