Search: id:A060900
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%I A060900
%S A060900 1,2,7,21,78,260,988,3458,13300,47880,185535,680295,2649570,9841260,
%T A060900 38470380,144263925,565514586,2136388436,8392954570,31893227366,
%U A060900 125515281892,479240167224,1888770070824,7240285271492
%N A060900 Number of walks of length n on square lattice, starting at origin, staying 
               on points with x >= 0, y <= x.
%F A060900 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).
%F A060900 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]
%F A060900 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]
%Y A060900 Cf. A005566, A001700, A060897-A060899.
%Y A060900 Sequence in context: A052911 A126133 A127540 this_sequence A151289 A150300 
               A150301
%Y A060900 Adjacent sequences: A060897 A060898 A060899 this_sequence A060901 A060902 
               A060903
%K A060900 nonn
%O A060900 0,2
%A A060900 David W. Wilson (davidwwilson(AT)comcast.net), May 05 2001
%E A060900 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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