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A025607
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Number of n-move rook paths on 8 X 8 board from given corner to same corner.
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3
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1, 0, 14, 84, 896, 10080, 127904, 1708224, 23426816, 325032960, 4532831744, 63353816064, 886318555136, 12404650352640, 173642248822784, 2430854346031104, 34031138021113856, 476430995352453120, 6670004313281921024, 93379882656019513344, 1307317290804734590976
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OFFSET
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0,3
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COMMENTS
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Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019
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LINKS
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FORMULA
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G.f.: (1 - 18*x + 58*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).
a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3. - Andrew Howroyd, Nov 05 2019
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MATHEMATICA
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CoefficientList[ Series[(1 - 18 x + 58 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]
LinearRecurrence[{18, -44, -168}, {1, 0, 14}, 30] (* Harvey P. Dale, Feb 13 2023 *)
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PROG
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(PARI) Vec((1 - 18*x + 58*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)) \\ Andrew Howroyd, Nov 05 2019
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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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EXTENSIONS
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STATUS
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approved
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