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%I #16 Mar 25 2023 13:21:41
%S 1,2,4,8,14,24,40,65,104,164,258,404,632,986,1537,2394,3728,5804,9034,
%T 14060,21880,34049,52984,82448,128294,199632,310636,483362,752129,
%U 1170338,1821084,2833664,4409270,6860960,10675864,16611969,25848728,40221404,62585722,97385276
%N Expansion of g.f.: (1+2*x^3+2*x^6)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)).
%H G. C. Greubel, <a href="/A084683/b084683.txt">Table of n, a(n) for n = 0..1000</a>
%H J. Hietarinta and C.-M. Viallet, <a href="https://doi.org/10.1016/S0960-0779(98)00266-5">Discrete Painlevé I and singularity confinement in projective space</a>, Chaos, Solitons and Fractals 11, 2000, p. 29.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,0,-2,1).
%t CoefficientList[Series[(1+2x^3+2x^6)/((1-x)(1-x-x^2+x^3-x^4-x^5+x^6)),{x,0,60}],x] (* or *) LinearRecurrence[{2,0,-2,2,0,-2,1},{1,2,4,8,14,24,40},60] (* _Harvey P. Dale_, Jun 23 2018 *)
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+2*x^3+2*x^6)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)) )); // _G. C. Greubel_, Mar 22 2023
%o (SageMath)
%o def A084683_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1+2*x^3+2*x^6)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)) ).list()
%o A084683_list(60) # _G. C. Greubel_, Mar 22 2023
%Y Cf. A064864.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 16 2003
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