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 A077950 #40 Sep 08 2022 08:45:08
%S A077950 1,1,1,-1,-3,-5,-3,3,13,19,13,-13,-51,-77,-51,51,205,307,205,-205,
%T A077950 -819,-1229,-819,819,3277,4915,3277,-3277,-13107,-19661,-13107,13107,
%U A077950 52429,78643,52429,-52429,-209715,-314573,-209715,209715,838861,1258291,838861,-838861,-3355443,-5033165,-3355443
%N A077950 Expansion of 1/(1-x+2*x^3).
%H A077950 G. C. Greubel, <a href="/A077950/b077950.txt">Table of n, a(n) for n = 0..1000</a>
%H A077950 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, -2).
%F A077950 a(n) = a(n-1) - 2*a(n-3), where a(0)=1, a(1)=1, a(2)=1. - _Sergei N. Gladkovskii_, Aug 21 2012
%F A077950 a(n) = (-1)^n * A077973(n). - _Ralf Stephan_, Aug 18 2013
%F A077950 G.f.: G(0)/(2*(1-x^2)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 25 2013
%F A077950 a(n) = Sum_{k=1..floor((n+2)/2)} binomial(n+2-2*k, k-1)*(-2)^(k-1). - _Taras Goy_, Sep 18 2019
%t A077950 CoefficientList[Series[1/(1-x+2x^3),{x,0,50}],x] (* or *) LinearRecurrence[ {1,0,-2}, {1,1,1},50] (* _Harvey P. Dale_, Oct 18 2013 *)
%o A077950 (PARI) Vec(1/(1-x+2*x^3)+O(x^50)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A077950 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+2*x^3) )); // _G. C. Greubel_, Jul 03 2019
%o A077950 (Sage) (1/(1-x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 03 2019
%o A077950 (GAP) a:=[1,1,1];; for n in [4..50] do a[n]:= a[n-1]-2*a[n-3]; od; a; # _G. C. Greubel_, Jul 03 2019
%Y A077950 Cf. A077973.
%K A077950 sign,easy
%O A077950 0,5
%A A077950 _N. J. A. Sloane_, Nov 17 2002, Jun 17 2007