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%I #18 May 21 2024 15:20:33
%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,-210944,153600,
%U 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="/A077988/b077988.txt">Table of n, a(n) for n = 0..1000</a>
%H J. Pan, <a href="https://cs.uwaterloo.ca/journals/JIS/OL13/Pan/pan8.html">Multiple Binomial Transforms and Families of Integer Sequences </a>, J. Int. Seq. 13 (2010), 10.4.2, T^(-1).
%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 * A077940(n). - _G. C. Greubel_, Jun 25 2019
%t LinearRecurrence[{-2, 0, 2}, {1, -2, 4}, 50] (* _Vladimir Joseph Stephan Orlovsky_, May 25 2011 *)
%t CoefficientList[Series[1/(1+2x-2x^3),{x,0,50}],x] (* _Harvey P. Dale_, May 21 2024 *)
%o (PARI) my(x='x+O('x^50)); Vec(1/(1+2*x-2*x^3)) \\ _G. C. Greubel_, Jun 25 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+2*x-2*x^3) )); // _G. C. Greubel_, Jun 25 2019
%o (Sage) (1/(1+2*x-2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 25 2019
%o (GAP) a:=[1,-2,4];; for n in [4..50] do a[n]:=-2*a[n-1]+2*a[n-3]; od; a; # _G. C. Greubel_, Jun 25 2019
%Y Cf. A000073, A001590, A000213, A077940, A135491.
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 17 2002
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