%I #17 Sep 22 2025 16:00:40

%S 1,-2,5,-14,37,-98,261,-694,1845,-4906,13045,-34686,92229,-245234,

%T 652069,-1733830,4610197,-12258362,32594581,-86667918,230447141,

%U -612751362,1629285701,-4332217046,11519222517,-30629233482,81442123573,-216551925662,575804441861,-1531045056530

%N Expansion of 1/(1+2*x-x^2+2*x^3).

%H G. C. Greubel, <a href="/A077987/b077987.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 (-2,1,-2).

%F a(n) = -2*a(n-1)+a(n-2)-2*a(n-3) with a(0)=1, a(1)=-2, a(2)=5. - _Harvey P. Dale_, Dec 27 2013

%F a(n) = (-1)^n * A077938(n). - _G. C. Greubel_, Jun 25 2019

%t CoefficientList[Series[1/(1+2x-x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{-2,1,-2},{1,-2,5},40] (* _Harvey P. Dale_, Dec 27 2013 *)

%o (PARI) Vec(1/(1+2*x-x^2+2*x^3)+O(x^40)) \\ _Charles R Greathouse IV_, Sep 27 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+2*x-x^2+2*x^3) )); // _G. C. Greubel_, Jun 25 2019

%o (SageMath) (1/(1+2*x-x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 25 2019

%o (GAP) a:=[1,-2,5];; 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 25 2019

%Y Cf. A077938.

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002