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A077913 Expansion of 1/((1-x)*(1+x+2*x^2+x^3)). 1

%I

%S 1,0,-1,1,2,-2,-2,5,2,-9,1,16,-8,-24,25,32,-57,-31,114,6,-202,77,322,

%T -273,-447,672,496,-1392,-271,2560,-625,-4223,2914,6158,-7762,-7467,

%U 16834,5863,-32063,3504,54760,-29704,-83319,87968,108375,-200991,-103726,397334,11110,-702051,282498,1110495

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

%H G. C. Greubel, <a href="/A077913/b077913.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,-1,1,1).

%F G.f.: 1-x^2/(U(0)+x^2) where U(k)= 1 + (1+x)*x/( 1 - (1+x)*x/((1+x)*x + 1/U(k+1))) ; (continued fraction, 2-step). - _Sergei N. Gladkovskii_, Oct 24 2012

%F 5*a(n) = 1 + 4*A077979(n) + 3*A077979(n-1) + A077979(n-2). - _R. J. Mathar_, Jul 10 2013

%t LinearRecurrence[{0,-1,1,1}, {1,0,-1,1}, 60] (* or *) CoefficientList[ Series[1/((1-x)*(1+x+2*x^2+x^3)), {x,0,60}], x] (* _G. C. Greubel_, Jul 02 2019 *)

%o (PARI) my(x='x+O('x^60)); Vec(1/((1-x)*(1+x+2*x^2+x^3))) \\ _G. C. Greubel_, Jul 02 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1+x+2*x^2+x^3)) )); // _G. C. Greubel_, Jul 02 2019

%o (Sage) (1/((1-x)*(1+x+2*x^2+x^3))).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 02 2019

%o (GAP) a:=[1,0,-1,1];; for n in [5..60] do a[n]:=-a[n-2]+a[n-3]+a[n-4]; od; a; # _G. C. Greubel_, Jul 02 2019

%K sign,easy

%O 0,5

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

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Last modified August 1 14:44 EDT 2021. Contains 346393 sequences. (Running on oeis4.)