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 A133190 #26 Dec 16 2023 17:58:09
%S A133190 1,3,3,5,13,27,51,101,205,411,819,1637,3277,6555,13107,26213,52429,
%T A133190 104859,209715,419429,838861,1677723,3355443,6710885,13421773,
%U A133190 26843547,53687091,107374181,214748365,429496731,858993459,1717986917,3435973837
%N A133190 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3).
%H A133190 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2).
%F A133190 From _R. J. Mathar_, Jan 13 2008: (Start)
%F A133190 O.g.f.: (2*x+1)*(x-1)/((2*x-1)*(x^2+1)).
%F A133190 a(n) = (4*2^n + (-1)^floor(n/2)*A010688(n))/5. (End)
%p A133190 A010688 := proc(n) if n mod 2 = 0 then 1; else 7; fi ; end:
%p A133190 A133190 := proc(n) (4*2^n+(-1)^floor(n/2)*A010688(n))/5 ; end:
%p A133190 seq(A133190(n),n=0..30) ; # _R. J. Mathar_, Jan 13 2008
%t A133190 LinearRecurrence[{2,-1,2},{1,3,3},40] (* _Harvey P. Dale_, Jun 22 2022 *)
%K A133190 nonn,easy
%O A133190 0,2
%A A133190 _Paul Curtz_, Dec 17 2007