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A292054
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Wiener index of the n X n knight graph.
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1
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288, 708, 1580, 3144, 5804, 9996, 16388, 25660, 38808, 56808, 81048, 112856, 154080, 206448, 272332, 353920, 454172, 575784, 722372, 897196, 1104592, 1348436, 1633848, 1965376, 2348992, 2789964, 3295180, 3870688, 4524356, 5263060, 6095716, 7030084, 8076192
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OFFSET
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4,1
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COMMENTS
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The square knight graph is connected for n >= 4.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,-1,2,2,-1,0,-3,1,2,-1).
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FORMULA
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a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) - a(n-5) + 2*a(n-6) + 2*a(n-7) - a(n-8) - 3*a(n-10) + a(n-11) + 2*a(n-12) - a(n-13) for n > 17.
G.f.: 4*x^4*(72 + 33*x - 31*x^2 + 35*x^3 + 15*x^4 + 68*x^5 + 39*x^6 - 28*x^7 - 14*x^8 - 60*x^9 + 37*x^10 + 36*x^11 - 26*x^12 + 2*x^13) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Sep 18 2017
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MATHEMATICA
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Join[{288}, LinearRecurrence[{2, 1, -3, 0, -1, 2, 2, -1, 0, -3, 1, 2, -1}, {708, 1580, 3144, 5804, 9996, 16388, 25660, 38808, 56808, 81048, 112856, 154080, 206448}, 20]]
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PROG
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(PARI) Vec(4*x^4*(72 + 33*x - 31*x^2 + 35*x^3 + 15*x^4 + 68*x^5 + 39*x^6 - 28*x^7 - 14*x^8 - 60*x^9 + 37*x^10 + 36*x^11 - 26*x^12 + 2*x^13) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)) + O(x^50)) \\ Colin Barker, Sep 18 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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