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

0,2

Links

Table of n, a(n) for n=0..19.

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 <hal-01225710v3>. See App. A.

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

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 *)

Crossrefs

Cf. A239112.

Sequence in context: A287222 A216598 A219397 * A337870 A181914 A089624

Adjacent sequences: A275909 A275910 A275911 * A275913 A275914 A275915

Keyword

nonn

Author

N. J. A. Sloane, Aug 26 2016

Status

approved