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.
%I A083322 #50 Jan 30 2024 17:39:41
%S A083322 1,2,6,11,22,42,85,170,342,683,1366,2730,5461,10922,21846,43691,87382,
%T A083322 174762,349525,699050,1398102,2796203,5592406,11184810,22369621,
%U A083322 44739242,89478486,178956971,357913942,715827882,1431655765,2863311530,5726623062
%N A083322 a(n) = 2^n - A081374(n).
%H A083322 Vincenzo Librandi, <a href="/A083322/b083322.txt">Table of n, a(n) for n = 1..1000</a>
%H A083322 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,2).
%F A083322 G.f.: x*(1+2*x^2) / ( (1-2*x)*(1+x)*(1-x+x^2) ). - _R. J. Mathar_, May 27 2011
%F A083322 From _Paul Curtz_, May 27 2011: (Start)
%F A083322 a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4).
%F A083322 a(n)+a(n+3) = 3*2^(n+1) = A007283(n+1).
%F A083322 a(n+6)-a(n) = 21*2^(n+1) = A175805(n+1).
%F A083322 (End)
%t A083322 CoefficientList[Series[(1 + 2 x^2) / ((1 - 2 x) (1 + x) (1 - x + x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 08 2016 *)
%t A083322 LinearRecurrence[{2,0,-1,2},{1,2,6,11},40] (* _Harvey P. Dale_, Jan 30 2024 *)
%o A083322 (Magma) I:=[1,2,6,11]; [n le 4 select I[n] else 2*Self(n-1)-Self(n-3)+2*Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 08 2016
%Y A083322 Cf. A081374.
%Y A083322 Trisections: A082365, A007613, A132804.
%K A083322 nonn,easy
%O A083322 1,2
%A A083322 _David Applegate_, Aug 22 2003