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A013991
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Number of edge-disjoint paths between opposite corners of a 2 X n grid.
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6
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1, 1, 4, 16, 72, 335, 1562, 7273, 33850, 157534, 733148, 3412005, 15879172, 73900265, 343925312, 1600598044, 7449042040, 34667184251, 161338016046, 750852888177, 3494403076902, 16262643529850, 75684907767980, 352230881365025, 1639251436594792, 7628931517771089
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OFFSET
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0,3
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REFERENCES
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rec.puzzles Dec 10 1995.
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LINKS
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Matthew House, Table of n, a(n) for n = 0..1491
Index entries for linear recurrences with constant coefficients, signature (6,-6,-4,16,-16,7).
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FORMULA
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G.f.: (-7*x^6+15*x^5-12*x^4+2*x^3+4*x^2-5*x+1)/[(1-x+x^2)*(1-5*x+9*x^3-7*x^4)].
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MATHEMATICA
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Join[{1}, LinearRecurrence[{6, -6, -4, 16, -16, 7}, {1, 4, 16, 72, 335, 1562}, 25]] (* Vincenzo Librandi, Sep 18 2018 *)
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PROG
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(PARI) Vec((-7*x^6+15*x^5-12*x^4+2*x^3+4*x^2-5*x+1)/((1-x+x^2)*(1-5*x+9*x^3-7*x^4)) + O(x^30)) \\ Michel Marcus, Sep 18 2018
(MAGMA) I:=[1, 1, 4, 16, 72, 335, 1562]; [n le 7 select I[n] else 6*Self(n-1) - 6*Self(n-2) - 4*Self(n-3) + 16*Self(n-4) - 16*Self(n-5) + 7*Self(n-6): n in [1..30]]; // Vincenzo Librandi, Sep 18 2018
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CROSSREFS
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Cf. A013990, A013992, A013993, A013994, A013995, A013996, A013997.
Sequence in context: A158784 A180141 A226282 * A151245 A151246 A152807
Adjacent sequences: A013988 A013989 A013990 * A013992 A013993 A013994
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KEYWORD
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nonn,easy
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AUTHOR
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Dan Hoey
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EXTENSIONS
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More terms from Matthew House, Dec 24 2016
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STATUS
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approved
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