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%I #17 Jan 15 2018 10:22:01
%S 1,2,16,166,1934,24076,312900,4191528,57424848,800511928,11314617512,
%T 161736519334,2333709074866,33940921354676,496985854805560,
%U 7320036386083320,108370564070861790,1611667048718909412,24065028942496468872,360628842425757805380
%N G.f. is square root of g.f. for A239112.
%H M. Bousquet-Mélou, <a href="http://arxiv.org/abs/1511.02111">Plane lattice walks avoiding a quadrant</a>, arXiv:1511.02111 [math.CO], 2015. See App. A.
%H Mireille Bousquet-Mélou, <a href="https://doi.org/10.1016/j.jcta.2016.06.010">Square lattice walks avoiding a quadrant</a>, Journal of Combinatorial Theory, Series A, Elsevier, 2016, Special issue for the 50th anniversary of the journal, 144, pp. 37-79. Also <hal-01225710v3>. See App. A.
%F Recurrence: (n-1)*n*(3*n - 2)*(3*n - 1)*a(n) = 8*(n-1)^2*(36*n^2 - 72*n + 25)*a(n-1) - 16*(2*n - 5)*(2*n - 1)*(6*n - 11)*(6*n - 7)*a(n-2). - _Vaclav Kotesovec_, Sep 08 2016
%F a(n) ~ 2^(4*n-1/3) / (sqrt(3) * Gamma(2/3) * n^(4/3)) * (1 - sqrt(3)*Gamma(2/3)^2 / (Pi*2^(1/3)*n^(1/3))). - _Vaclav Kotesovec_, Sep 08 2016
%t CoefficientList[Series[Sqrt[-2 + 64*x + Sqrt[1 - 256*x + 4096*x^2 + 12*(x - 16*x^2)^(1/3)] + (1/2)*Sqrt[-24 + 32*(1 - 32*x)^2 - 48*(x - 16*x^2)^(1/3) + (8*(1 + 480*x - 24576*x^2 + 262144*x^3)) / Sqrt[1 - 256*x + 4096*x^2 + 12*(x - 16*x^2)^(1/3)]]], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Sep 08 2016 *)
%Y Cf. A239112.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Aug 26 2016
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