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A058920
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a(n) = 2n^4 + 2n^3 + 3n^2 + 2n + 1.
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1
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1, 10, 65, 250, 697, 1586, 3145, 5650, 9425, 14842, 22321, 32330, 45385, 62050, 82937, 108706, 140065, 177770, 222625, 275482, 337241, 408850, 491305, 585650, 692977, 814426, 951185, 1104490, 1275625, 1465922, 1676761, 1909570, 2165825
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OFFSET
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0,2
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COMMENTS
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On a 2n X (n^2 - n + 1) X n^2 cuboid (with n >= 3) there are six pairs of points with the maximum surface distance between them: the four pairs of opposite corners and the opposite pairs of points on the smallest faces 1 in from the midpoints of the shortest edges; this maximum surface distance is sqrt(a(n)).
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LINKS
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FORMULA
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G.f.: (1+5*x+25*x^2+15*x^3+2*x^4)/(1-5*x+10*x^2-10*x^3+5*x^4-x^5). - Colin Barker, Jan 01 2012
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MATHEMATICA
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Table[2n^4+2n^3+3n^2+2n+1, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 65, 250, 697}, 40] (* Harvey P. Dale, Dec 17 2017 *)
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PROG
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(PARI) for (n = 0, 500, write("b058920.txt", n, " ", 2*n^4 + 2*n^3 + 3*n^2 + 2*n + 1); ) \\ Harry J. Smith, Jun 24 2009
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CROSSREFS
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For n >= 2 the sequence is a subsequence of A007692.
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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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