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%I #21 Sep 08 2022 08:45:08
%S 1,-1,-1,2,1,-4,0,7,-3,-11,10,15,-24,-16,49,7,-89,26,145,-108,-208,
%T 279,245,-595,-174,1119,-176,-1888,1121,2831,-3185,-3598,7137,3244,
%U -13920,295,24301,-10971,-37926,35567,51256,-84464,-53615,171287,20407,-309366,97265,501060,-386224,-713161
%N Expansion of 1/(1+x+2*x^2+x^3).
%H G. C. Greubel, <a href="/A077979/b077979.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,-1).
%F G.f.: 1 - x/(G(0) + x) where G(k)= 1 - x*(k+1)/(1 - 1/(1 + (k+1)/G(k+1)));(continued fraction, 3-step). - _Sergei N. Gladkovskii_, Nov 17 2012
%F a(n) = (-1)^n*A077954(n). - _R. J. Mathar_, Jul 10 2013
%t CoefficientList[Series[1/(1+x+2x^2+x^3),{x,0,50}],x] (* or *) LinearRecurrence[ {-1,-2,-1},{1,-1,-1},50] (* _Harvey P. Dale_, Apr 18 2016 *)
%o (PARI) my(x='x+O('x^50)); Vec(1/(1+x+2*x^2+x^3)) \\ _G. C. Greubel_, Jun 25 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x+2*x^2+x^3) )); // _G. C. Greubel_, Jun 25 2019
%o (Sage) (1/(1+x+2*x^2+x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 25 2019
%o (GAP) a:=[1,-1,-1];; for n in [4..50] do a[n]:=-a[n-1]-2*a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Jun 25 2019
%Y Cf. A077954.
%K sign,easy
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002
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