OFFSET
0,2
REFERENCES
Mireille Bousquet-Mélou and Gilles Schaeffer, Counting walks on the slit plane (extended abstract). Mathematics and computer science (Versailles, 2000), 101-112, Trends Math., Birkhäuser, Basel, 2000.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
M. Bousquet-Mélou and Gilles Schaeffer, Walks on the slit plane, Probability Theory and Related Fields, Vol. 124, no. 3 (2002), 305-344.
FORMULA
G.f.: ((1+4*t)^(1/4)*(1+sqrt(1-16*t^2))^(1/2))/(sqrt(2)*(1-4*t)^(3/4)).
Contribution from Vaclav Kotesovec, Oct 24 2012: (Start)
G.f.: 1/2*((1+4*x)/(1-4*x))^(1/4)*(1+sqrt((1+4*x)/(1-4*x))).
Recurrence: (n-1)*n*a(n) = 8*(n-1)*a(n-1) + 4*(8*n^2-32*n+29)*a(n-2) - 128*(n-3)*a(n-3) - 256*(n-4)*(n-3)*a(n-4).
a(n) ~ 2^(2*n-1/4)/(Gamma(3/4)*n^(1/4)).
(End)
MATHEMATICA
CoefficientList[Series[1/2*((1+4*x)/(1-4*x))^(1/4)*(1+Sqrt[(1+4*x)/(1-4*x)]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mireille Bousquet-Mélou, Mar 27 2000
STATUS
approved