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

%I #14 Sep 08 2022 08:45:08

%S 1,1,0,-3,-7,-8,1,25,56,61,-15,-208,-447,-463,176,1725,3561,3496,

%T -1855,-14263,-28312,-26243,18401,117600,224641,195681,-175520,

%U -967043,-1778727,-1447848,1628801,7932025,14054296,10615741,-14809135,-64904048,-110805567,-76993903,132527376

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

%H G. C. Greubel, <a href="/A078004/b078004.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,-2,-1).

%F G.f.: (1-x)/(1-2*x+2*x^2+x^3).

%F a(n) = 2*a(n-1) - 2*a(n-2) - a(n-3). - _Wesley Ivan Hurt_, Jul 29 2022

%t LinearRecurrence[{2,-2,-1}, {1,1,0}, 40] (* or *) CoefficientList[ Series[(1-x)/(1-2*x+2*x^2+x^3), {x,0,40}], x] (* _G. C. Greubel_, Jun 27 2019 *)

%o (PARI) my(x='x+O('x^40)); Vec((1-x)/(1-2*x+2*x^2+x^3)) \\ _G. C. Greubel_, Jun 27 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/( 1-2*x+2*x^2+x^3) )); // _G. C. Greubel_, Jun 27 2019

%o (Sage) ((1-x)/(1-2*x+2*x^2+x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 27 2019

%o (GAP) a:=[1,1,0];; for n in [4..40] do a[n]:=2*a[n-1]-2*a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Jun 27 2019

%K sign,easy

%O 0,4

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