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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
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 (list; graph; refs; listen; history; text; internal format)
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., Birkhaeuser, 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 * A045627 A007722 A149008

Adjacent sequences:  A053788 A053789 A053790 * A053792 A053793 A053794

KEYWORD

nonn

AUTHOR

Mireille Bousquet-Mélou, Mar 27 2000

STATUS

approved

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Last modified March 28 05:07 EDT 2017. Contains 284182 sequences.