A053791 Number of walks of length n on the square lattice that start from (0,0) and do not touch the nonpositive real axis once they have left their starting point.

1, 3, 9, 34, 121, 468, 1742, 6802, 25841, 101428, 389820, 1535138, 5944054, 23461802, 91314038, 361034640, 1410482689, 5583955632, 21878361324, 86703276854, 340483274100, 1350453786234, 5312965594054, 21087370402596, 83087565741142, 329971068701702

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

Table of n, a(n) for n=0..25.

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+sqrt(1+4*t))^(1/2)*(1+sqrt(1-4*t))^(1/2))/(2*(1-4*t)^(3/4)).

Mathematica

CoefficientList[ Sqrt[(1+Sqrt[1-4*t])*(1+Sqrt[1+4*t])]/(2*(1-4*t)^(3/4))+O[t]^30, t] (* Jean-François Alcover, Jun 19 2015 *)

Crossrefs

Cf. A000108, A053792.

Sequence in context: A149005 A149006 A149007 * A296223 A045627 A007722

Adjacent sequences: A053788 A053789 A053790 * A053792 A053793 A053794

Keyword

nonn

Author

Mireille Bousquet-Mélou, Mar 27 2000

Status

approved