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 A077989 #13 Sep 08 2022 08:45:08
%S A077989 1,-2,3,-2,-3,14,-29,38,-19,-58,211,-402,477,-130,-1021,3126,-5491,
%T A077989 5814,115,-17026,45565,-73874,68131,28742,-273363,654246,-977645,
%U A077989 754318,777501,-4264610,9260355,-12701098,7612621,15996566,-65007949,129244574,-161488067,63715662,292545891
%N A077989 Expansion of 1/(1+2*x+x^2-2*x^3).
%H A077989 G. C. Greubel, <a href="/A077989/b077989.txt">Table of n, a(n) for n = 0..1000</a>
%H A077989 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1,2).
%F A077989 a(n) = (-1)^n * A077942(n). - _G. C. Greubel_, Jun 26 2019
%F A077989 a(n) = (-1)^n*Sum_{k=0..(n+1)/2} binomial(n+1-k,2k+1)*(-2)^k, n>=0. - _Taras Goy_, Apr 15 2020
%t A077989 LinearRecurrence[{-2,-1,2}, {1,-2,3}, 40] (* or *) CoefficientList[Series[1/(1+2*x+x^2-2*x^3), {x,0,40}], x] (* _G. C. Greubel_, Jun 26 2019 *)
%o A077989 (PARI) my(x='x+O('x^40)); Vec(1/(1+2*x+x^2-2*x^3)) \\ _G. C. Greubel_, Jun 26 2019
%o A077989 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+2*x+x^2-2*x^3) )); // _G. C. Greubel_, Jun 26 2019
%o A077989 (Sage) (1/(1+2*x+x^2-2*x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 26 2019
%o A077989 (GAP) a:=[1,-2,3];; for n in [4..40] do a[n]:=-2*a[n-1]-a[n-2]+2*a[n-3]; od; a; # _G. C. Greubel_, Jun 26 2019
%Y A077989 Cf. A077942.
%K A077989 sign,easy
%O A077989 0,2
%A A077989 _N. J. A. Sloane_, Nov 17 2002