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A296196
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Harary index of the n X n queen graph.
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0
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0, 6, 32, 98, 230, 460, 826, 1372, 2148, 3210, 4620, 6446, 8762, 11648, 15190, 19480, 24616, 30702, 37848, 46170, 55790, 66836, 79442, 93748, 109900, 128050, 148356, 170982, 196098, 223880, 254510, 288176, 325072, 365398, 409360, 457170, 509046, 565212, 625898, 691340
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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*(n - 1)*(3*n^2 + 13*n - 2)/12.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: 2*x^2*(-3 - x + x^2)/(-1 + x)^5.
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MATHEMATICA
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Table[n (n - 1) (3 n^2 + 13 n - 2)/12, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 6, 32, 98, 230}, 40]
CoefficientList[Series[2 x (-3 - x + x^2)/(-1 + x)^5, {x, 0, 20}], x]
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PROG
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(PARI) first(n) = Vec(2*x^2*(-3 - x + x^2)/(-1 + x)^5 + O(x^(n+1)), -n) \\ Iain Fox, Dec 07 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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