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%I #25 Feb 06 2024 08:13:37
%S 1,1,3,25,75,289,1283,4905,19547,79281,315123,1260153,5049419,
%T 20180865,80722531,322959049,1291700027,5166801489,20667742419,
%U 82669888537,330679592235,1322722573857,5290881765955,21163527357033,84654142731803
%N Expansion of (1 - 4*x^2 - 8*x^3)/((1 + 2*x + 4*x^2)*(1 - x - 2*x - 4*x^2 - 4*x^3 + 16*x^4)).
%H G. C. Greubel, <a href="/A129443/b129443.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,24,8,-16,-64).
%F G.f.: (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3)).
%p (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3));
%p taylor(%,x=0,10) ; # _R. J. Mathar_, Sep 09 2011
%t p[x_, q_]= (1-q^2*x^2-q^3*x^3)/((1+q*x+q^2*x^2)*(1-x-q*x-q^2*x^2- q^2*x^3+q^4*x^4));
%t CoefficientList[Series[p[x,2], {x,0,40}], x]
%t LinearRecurrence[{1,6,24,8,-16,-64}, {1,1,3,25,75,289}, 40] (* _G. C. Greubel_, Feb 06 2024 *)
%o (PARI) Vec((1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3)) )); // _G. C. Greubel_, Feb 06 2024
%o (SageMath)
%o def A129443_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-4*x^2-8*x^3)/((1+2*x+4*x^2)*(1-4*x)*(1+x-4*x^3)) ).list()
%o A129443_list(40) # _G. C. Greubel_, Feb 06 2024
%Y Cf. A129441.
%K nonn,easy,less
%O 0,3
%A _Roger L. Bagula_, Jun 08 2007
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