A078014 - OEIS

%I #17 Sep 08 2022 08:45:08

%S 1,0,0,-2,-2,-2,2,6,10,6,-6,-26,-38,-26,26,102,154,102,-102,-410,-614,

%T -410,410,1638,2458,1638,-1638,-6554,-9830,-6554,6554,26214,39322,

%U 26214,-26214,-104858,-157286,-104858,104858,419430,629146,419430,-419430,-1677722,-2516582,-1677722,1677722

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

%H G. C. Greubel, <a href="/A078014/b078014.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 (1,0,-2).

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

%F G.f.: G(0)/(2*(1+x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 25 2013

%F a(n) = A077950(n) - A077950(n-1). - _R. J. Mathar_, Jul 21 2016

%t LinearRecurrence[{1,0,-2}, {1,0,0}, 50] (* or *) CoefficientList[Series[ (1-x)/(1-x+2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Jun 29 2019 *)

%o (PARI) my(x='x+O('x^50)); Vec((1-x)/(1-x+2*x^3)) \\ _G. C. Greubel_, Jun 29 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^3) )); // _G. C. Greubel_, Jun 29 2019

%o (Sage) ((1-x)/(1-x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 29 2019

%o (GAP) a:=[1,0,0];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-3]; od; a; # _G. C. Greubel_, Jun 29 2019

%Y Cf. A077950.

%K sign,easy

%O 0,4

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