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 A078021 #11 Sep 08 2022 08:45:08
%S A078021 1,0,-2,-3,1,9,10,-9,-38,-30,55,153,73,-288,-587,-84,1378,2133,-539,
%T A078021 -6183,-7238,5667,26326,22230,-36089,-106875,-56927,192912,413641,
%U A078021 84744,-935450,-1518579,267577,4240185,5223610,-3524337,-18211742,-16386678,23561143,74546241,43810633,-128842992
%N A078021 Expansion of (1-x)/(1-x+2*x^2+x^3).
%H A078021 G. C. Greubel, <a href="/A078021/b078021.txt">Table of n, a(n) for n = 0..1000</a>
%H A078021 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,-1).
%F A078021 a(n) = A077978(n) - A077978(n-1). - _G. C. Greubel_, Jun 29 2019
%F A078021 a(n) = a(n-1)-2*a(n-2)-a(n-3). - _Wesley Ivan Hurt_, Apr 26 2021
%t A078021 LinearRecurrence[{1,-2,-1}, {1,0,-2}, 50] (* or *) CoefficientList[ Series[(1-x)/(1-x+2*x^2+x^3), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 29 2019 *)
%o A078021 (PARI) my(x='x+O('x^50)); Vec((1-x)/(1-x+2*x^2+x^3)) \\ _G. C. Greubel_, Jun 29 2019
%o A078021 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^2+x^3) )); // _G. C. Greubel_, Jun 29 2019
%o A078021 (Sage) ((1-x)/(1-x+2*x^2+x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 29 2019
%o A078021 (GAP) a:=[1,0,-2];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Jun 29 2019
%Y A078021 Cf. A077978.
%K A078021 sign
%O A078021 0,3
%A A078021 _N. J. A. Sloane_, Nov 17 2002