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A292059
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Wiener index of the n X n white bishop graph.
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0
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1, 8, 42, 104, 251, 464, 852, 1360, 2165, 3160, 4606, 6328, 8687, 11424, 15016, 19104, 24297, 30120, 37330, 45320, 55011, 65648, 78332, 92144, 108381, 125944, 146342, 168280, 193495, 220480, 251216, 283968, 320977, 360264, 404346, 450984, 502987, 557840, 618660, 682640
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OFFSET
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2,2
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LINKS
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Table of n, a(n) for n=2..41.
Eric Weisstein's World of Mathematics, White Bishop Graph
Eric Weisstein's World of Mathematics, Wiener Index
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).
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FORMULA
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a(n) = (3 + 2*n - 6*n^2 - 8*n^3 + 6*n^4 + 3*(-1)^n*(-1 - 2*n + 2*n^2))/24.
a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
G.f.: x^2*(-1 - 6*x - 24*x^2 - 10*x^3 - 7 x^4)/((-1 + x)^5*(1 + x)^3).
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MATHEMATICA
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Table[(3 + 2 n - 6 n^2 - 8 n^3 + 6 n^4 + 3 (-1)^n (-1 - 2 n + 2 n^2))/24, {n, 2, 20}]
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 8, 42, 104, 251, 464, 852, 1360}, 20]
CoefficientList[Series[(-1 - 6 x - 24 x^2 - 10 x^3 - 7 x^4)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]
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CROSSREFS
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Sequence in context: A204572 A086392 A234860 * A027903 A231069 A319235
Adjacent sequences: A292056 A292057 A292058 * A292060 A292061 A292062
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Sep 08 2017
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STATUS
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approved
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