A275912 G.f. is square root of g.f. for A239112.

1, 2, 16, 166, 1934, 24076, 312900, 4191528, 57424848, 800511928, 11314617512, 161736519334, 2333709074866, 33940921354676, 496985854805560, 7320036386083320, 108370564070861790, 1611667048718909412, 24065028942496468872, 360628842425757805380

Offset: 0

Author

N. J. A. Sloane, Aug 26 2016

Keywords

• nonn

Links

• M. Bousquet-Mélou, Plane lattice walks avoiding a quadrant, arXiv:1511.02111 [math.CO], 2015. See App. A.
• Mireille Bousquet-Mélou, Square lattice walks avoiding a quadrant, Journal of Combinatorial Theory, Series A, Elsevier, 2016, Special issue for the 50th anniversary of the journal, 144, pp. 37-79. Also . See App. A.

Crossrefs

Cf. A239112.

Programs

Mathematica

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 *)

Formula

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

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