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%I #12 Oct 07 2023 05:08:03
%S 1,0,1,2,4,11,28,75,207,579,1647,4744,13807,40550,120016,357613,
%T 1071916,3229870,9777767,29724593,90705886,277744244,853123473,
%U 2627968236,8116487286,25128482223,77971354506,242439732171
%N Expansion of g.f.: (1+x - sqrt(1-2*x-3*x^2-4*x^3))/(2+2*x+2*x^2).
%H G. C. Greubel, <a href="/A108629/b108629.txt">Table of n, a(n) for n = 1..1000</a>
%F Conjecture D-finite with recurrence: n*a(n) = (n-3)*a(n-1) +4*(n-3)*a(n-2) +3*(3*n-10)*a(n-3) +(7*n-27)*a(n-4) +2*(2*n-9)*a(n-5). - _R. J. Mathar_, Jan 24 2020
%t Rest@CoefficientList[Series[(1+x -Sqrt[1-2*x-3*x^2-4*x^3])/(2+2*x +2*x^2), {x, 0, 40}], x] (* _G. C. Greubel_, Oct 06 2023 *)
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1+x-Sqrt(1-2*x-3*x^2-4*x^3))/(2+2*x+2*x^2) )); // _G. C. Greubel_, Oct 06 2023
%o (SageMath)
%o def A108629_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1+x-sqrt(1-2*x-3*x^2-4*x^3))/(2+2*x+2*x^2) ).list()
%o a=A108629_list(41); a[1:] # _G. C. Greubel_, Oct 06 2023
%Y Cf. A039983.
%K nonn
%O 1,4
%A _Christian G. Bower_, Jun 12 2005
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