A077940 - OEIS

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

%S 1,2,4,6,8,8,4,-8,-32,-72,-128,-192,-240,-224,-64,352,1152,2432,4160,

%T 6016,7168,6016,0,-14336,-40704,-81408,-134144,-186880,-210944,

%U -153600,66560,555008,1417216,2701312,4292608,5750784,6098944,3612672,-4276224,-20750336,-48726016,-88899584

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

%H G. C. Greubel, <a href="/A077940/b077940.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 (2,0,-2).

%F a(n) = (-1)^n * A077988(n). - _R. J. Mathar_, Feb 04 2014

%t LinearRecurrence[{2,0,-2}, {1,2,4}, 50] (* or *) CoefficientList[Series[ 1/(1-2*x+2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Jun 26 2019 *)

%o (PARI) my(x='x+O('x^50)); Vec(1/(1-2*x+2*x^3)) \\ _G. C. Greubel_, Jun 26 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-2*x+2*x^3) )); // _G. C. Greubel_, Jun 26 2019

%o (Sage) (1/(1-2*x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 26 2019

%o (GAP) a:=[1,2,4];; for n in [4..50] do a[n]:=2*(a[n-1]-a[n-3]); od; a; # _G. C. Greubel_, Jun 26 2019

%Y Cf. A077988.

%K sign,easy

%O 0,2

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