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A337900
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The number of walks of length 2n on the square lattice that start from the origin (0,0) and end at the vertex (2,0).
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4
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1, 16, 225, 3136, 44100, 627264, 9018009, 130873600, 1914762564, 28210561600, 418151049316, 6230734868736, 93271169290000, 1401915345465600, 21147754404155625, 320042195924198400, 4857445984927644900, 73916947787011560000, 1127482124965160372100
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*4F3(3/2,3/2,2,2; 1,3,3; 16*x).
D-finite with recurrence (n-1)^2*(n+1)^2*a(n) -4*n^2*(2*n-1)^2*a(n-1)=0.
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EXAMPLE
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a(2)=16 counts the walks RRRL, RRLR, RLRR, LRRR, RRUD, RRDU, RDRU, RURD, RUDR, RDUR, URRD, DRRU, URDR, DRUR, UDRR, DURR of length 4.
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CROSSREFS
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KEYWORD
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nonn,easy,walk
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AUTHOR
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STATUS
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approved
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