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A242088
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Number of edges in the convex hull of a rigorous solution to Thomson's problem for n points.
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3
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OFFSET
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0,4
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COMMENTS
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Thomson’s problem is to determine the stable equilibrium configuration(s) of n particles confined to the surface of a sphere and repelling each other by an inverse square force.
Rigorous solutions are known only for n <= 6 and n = 12, with a(12) = 30.
Non-rigorous solutions are given in Wikipedia for all n <= 460. The least non-monotonic pair is 63 > 60 for n = 23 and 24, respectively.
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LINKS
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FORMULA
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a(n) <= n(n-1)/2 = (n choose 2).
a(n) <= 3*n-6 = A008585(n-2) for n >= 3, since a solution to Thomson's problem gives a planar graph, which has 3*n-6 edges if it is maximal (see A008486 comments). - Jonathan Sondow, Mar 03 2018 answering a question by Joseph Wheat.
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EXAMPLE
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For n = 0 or 1 points, the convex hull is empty or a point, so there are no edges and a(0) = a(1) = 0.
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CROSSREFS
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KEYWORD
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more,hard,nonn
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AUTHOR
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STATUS
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approved
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