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A060900
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Number of walks of length n on square lattice, starting at origin, staying on points with x >= 0, y <= x.
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7
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1, 2, 7, 21, 78, 260, 988, 3458, 13300, 47880, 185535, 680295, 2649570, 9841260, 38470380, 144263925, 565514586, 2136388436, 8392954570, 31893227366, 125515281892, 479240167224, 1888770070824, 7240285271492
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| The following conjectural formula for this sequence is apparently due to Ira Gessel: a(0) = 1, a(2n) = a(2n-1)*(12n+2)/(3n+1), a(2n+1) = a(2n)*(4n+2)/(n+1).
G.f.: (hypergeom([ -1/12, 1/4],[2/3],-64*x*(4*x+1)^2/(4*x-1)^4)-1)/(2*x) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 02 2009]
G.f.: (T(x)-1)/(2*x) where T(x) satisfies 27*(4*x-1)^2*T^8 - 18*(4*x-1)^2*T^4 - (128*x^2+192*x+8)*T^2 - (4*x-1)^2 = 0 [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 02 2009]
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CROSSREFS
| Cf. A005566, A001700, A060897-A060899.
Sequence in context: A126133 A186240 A127540 * A151289 A150300 A150301
Adjacent sequences: A060897 A060898 A060899 * A060901 A060902 A060903
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net), May 05 2001
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Doron Zeilberger, Sep 13 2007
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