%I #16 Sep 08 2022 08:45:07
%S 1,0,-1,2,1,-4,3,6,-11,0,23,-22,-23,68,-21,-114,157,72,-385,242,529,
%T -1012,-45,2070,-1979,-2160,6119,-1798,-10439,14036,6843,-34914,21229,
%U 48600,-91057,-6142,188257,-175972,-200541,552486,-151403,-953568,1256375,650762,-3163511,1861988,4465035
%N Expansion of 1/(1+x^2-2*x^3).
%C Equally, expansion of (1-x)^(-1)/(1+x+2*x^2).
%H G. C. Greubel, <a href="/A077912/b077912.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, -1, 2).
%F a(0)=1, a(1)=0, a(2)=-1, a(n) = -a(n-2)+2*a(n-3). - _Harvey P. Dale_, Dec 10 2012
%F a(n) = (-1)^n * A077963(n). - _G. C. Greubel_, Jun 23 2019
%t CoefficientList[Series[1/(1+x^2-2*x^3),{x,0,50}],x] (* or *) LinearRecurrence[{0,-1,2},{1,0,-1},50] (* _Harvey P. Dale_, Dec 10 2012 *)
%o (PARI) my(x='x+O('x^50)); Vec(1/(1+x^2-2*x^3)) \\ _G. C. Greubel_, Jun 23 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x^2-2*x^3) )); // _G. C. Greubel_, Jun 23 2019
%o (Sage) (1/(1+x^2-2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 23 2019
%o (GAP) a:=[1,0,-1];; for n in [4..50] do a[n]:=-a[n-2]+2*a[n-3]; od; a; # _G. C. Greubel_, Jun 23 2019
%Y Cf. A077963.
%K sign,easy
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002