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Search: id:A098070
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| A098070 |
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Consider a single king on an infinite chessboard. This sequence gives number of n-moves paths when king starting at origin reaches the origin again for the first time at step n. |
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1
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| 1, 0, 8, 24, 152, 816, 5320, 33840, 229144, 1560864, 10906576, 76962912, 550406472, 3969725856, 28875757200, 211436151456, 1557623566104, 11533972310976, 85802992349344, 640901090847360
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Traditionally for the "first passage time" problems use initial condition Gf(0)=0, but here we define Gf(0)=1 to make this sequence consistent with similar sequences already present in the database.
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FORMULA
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(Maple notation) Gf(x)=2-Pi/2*(1+4*x)/EllipticK(4*sqrt(x*(1+x))/(1+4*x))
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MAPLE
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G:=t->2-Pi*(1+4*t)/2/EllipticK(4*sqrt(t*(1+t))/(1+4*t)); G.f.:=convert(series(G(t), t, 30), polynom): seq(print(i, coeff(Gf, t, i)), i=0..degree(Gf));
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CROSSREFS
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Cf. A094061, A054474.
Sequence in context: A063515 A010566 A092771 this_sequence A100042 A061027 A052656
Adjacent sequences: A098067 A098068 A098069 this_sequence A098071 A098072 A098073
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KEYWORD
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nonn
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AUTHOR
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Sergey Perepechko (persn(AT)aport.ru), Sep 13 2004
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