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A292045
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Wiener index of the n X n X n grid graph.
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0
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0, 48, 972, 7680, 37500, 136080, 403368, 1032192, 2361960, 4950000, 9663060, 17791488, 31188612, 52437840, 85050000, 133693440, 204459408, 305165232, 445697820, 638400000, 898502220, 1244602128, 1699194552, 2289254400, 3046875000, 4009964400, 5223002148
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (n - 1)*(n + 1)*n^5/2.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
G.f.: 12*x^2*(4 + 49*x + 104*x^2 + 49*x^3 + 4*x^4)/(1 - x)^8.
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MATHEMATICA
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Table[(n - 1) (n + 1) n^5/2, {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 48, 972, 7680, 37500, 136080, 403368, 1032192}, 20]
CoefficientList[Series[12 x (4 + 49 x + 104 x^2 + 49 x^3 + 4 x^4)/(1 - x)^8, {x, 0, 20}], x]
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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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