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%I #18 Sep 08 2022 08:45:08
%S 1,-1,3,-7,15,-35,79,-179,407,-923,2095,-4755,10791,-24491,55583,
%T -126147,286295,-649755,1474639,-3346739,7595527,-17238283,39122815,
%U -88790435,201512631,-457339131,1037945263,-2355648787,5346217575,-12133405675,27537138399,-62496384899,141837473047
%N Expansion of 1/(1+x-2*x^2+2*x^3).
%H G. C. Greubel, <a href="/A077970/b077970.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 (-1, 2, -2).
%F a(n) = (-1)^n*A077946(n). - _R. J. Mathar_, Feb 28 2019
%t CoefficientList[Series[1/(1+x-2x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {-1,2,-2},{1,-1,3},40] (* _Harvey P. Dale_, Sep 29 2018 *)
%o (PARI) Vec(1/(1+x-2*x^2+2*x^3)+O(x^40)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+x-2*x^2+2*x^3) )); // _G. C. Greubel_, Jun 24 2019
%o (Sage) (1/(1+x-2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 24 2019
%o (GAP) a:=[1,1,-3];; for n in [4..40] do a[n]:=-a[n-1]+2*a[n-2]-2*a[n-3]; od; a; # _G. C. Greubel_, Jun 24 2019
%Y Cf. A077946, A078040.
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002