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A077910 Expansion of 1/((1-x)*(1+x+2*x^2-2*x^3)). 1

%I #11 Sep 08 2022 08:45:07

%S 1,0,-1,4,-1,-8,19,-4,-49,96,-5,-284,487,72,-1613,2444,927,-9040,

%T 12075,7860,-50089,58520,57379,-274596,276879,387072,-1490021,1269636,

%U 2484551,-8003864,5574035,15402796,-42558593,22901072,93021707,-223941036,83699767,550225720,-1165507325

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

%H G. C. Greubel, <a href="/A077910/b077910.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,4,-2).

%t CoefficientList[Series[1/((1-x)*(1+x+2x^2-2x^3)),{x,0,40}],x] (* _Harvey P. Dale_, Sep 12 2017 *)

%t LinearRecurrence[{0,-1,4,-2}, {1,0,-1,4}, 40] (* _G. C. Greubel_, Jul 02 2019 *)

%o (PARI) my(x='x+O('x^40)); Vec(1/((1-x)*(1+x+2*x^2-2*x^3))) \\ _G. C. Greubel_, Jul 02 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x)*(1+x+2*x^2-2*x^3)) )); // _G. C. Greubel_, Jul 02 2019

%o (Sage) (1/((1-x)*(1+x+2*x^2-2*x^3))).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 02 2019

%o (GAP) a:=[1,0,-1,4];; for n in [5..40] do a[n]:=-a[n-2]+4*a[n-2]-2*a[n-3]; od; a; # _G. C. Greubel_, Jul 02 2019

%K sign,easy

%O 0,4

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

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Last modified March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)