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%I #26 Sep 08 2022 08:45:08
%S 1,0,-2,1,4,-4,-7,12,10,-31,-8,72,-15,-152,102,289,-356,-476,1001,596,
%T -2478,-191,5552,-2096,-11295,9744,20494,-30783,-31244,82060,31705,
%U -195364,18650,422433,-232664,-826216,887761,1419768,-2601738,-1951775,6623244,1301812,-15198263,4019620
%N Expansion of 1/(1+2*x^2-x^3).
%H G. C. Greubel, <a href="/A077965/b077965.txt">Table of n, a(n) for n = 0..1000</a>
%H N. Gogin and A. Mylläri, <a href="http://math.unm.edu/~aca/ACA/2013/Nonstandard/Gogin.pdf">Padovan-like sequences and Bell polynomials</a>, Proceedings of Applications of Computer Algebra ACA, 2013.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,1).
%F a(0)=1, a(1)=0, a(2)=-2, a(n) = -2*a(n-2)+a(n-3). - _Harvey P. Dale_, Jan 22 2015
%F a(n) = (-1)^n * A077967(n). - _G. C. Greubel_, Jun 24 2019
%t CoefficientList[Series[1/(1+2x^2-x^3),{x,0,50}],x] (* or *) LinearRecurrence[ {0,-2,1},{1,0,-2},50] (* _Harvey P. Dale_, Jan 22 2015 *)
%o (PARI) my(x='x+O('x^50)); Vec(1/(1+2*x^2-x^3)) \\ _Altug Alkan_, Feb 20 2018
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+2*x^2-x^3) )); // _G. C. Greubel_, Jun 24 2019
%o (Sage) (1/(1+2*x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 24 2019
%o (GAP) a:=[1,0,-2];; for n in [4..50] do a[n]:=-2*a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Jun 24 2019
%Y Cf. A077967.
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002
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