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A053791
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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.
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1
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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
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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M. Bousquet-Mélou and Gilles Schaeffer, Walks on the slit plane, Probability Theory and Related Fields, Vol. 124, no. 3 (2002), 305-344.
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FORMULA
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G.f.: ((1+sqrt(1+4*t))^(1/2)*(1+sqrt(1-4*t))^(1/2))/(2*(1-4*t)^(3/4)).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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