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%I #12 Jun 01 2018 03:12:47
%S 12,24,12,48,20,16,12,16,4,120,4
%N Order of the symmetry group of the (in some cases conjectural) minimal-energy configuration of n identical charged particles confined to the surface of a sphere.
%C a(0), a(1) and a(2) are all infinite, because their symmetry groups are continuous (they contain rotations with arbitrary angles). Actual symmetry groups: 3 D_{3h}, 4 T_{d}, 5 D_{3h}, 6 O_{d}, 7 D_{5h}, 8 D_{4d}, 9 D_{3h}, 10 D_{4h}, 11 D_{1h}, 12 I_{d}, 13 D_{1h}.
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath005/kmath005.htm">Min-Energy Configurations of Electrons On A Sphere</a>, MathPages.
%H R. H. Hardin, N. J. A. Sloane and W. D. Smith, <a href="http://neilsloane.com/electrons/">Minimal Energy Configurations of Points on a Sphere</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Thomson_problem">Thomson Problem</a>.
%e a(3)=12 because the minimal-energy configuration of 3 charged particles on a sphere is an equilateral triangle on the equator, which has symmetry group D_3h of order 12.
%Y Cf. A033177, A242617.
%K nonn,more
%O 3,1
%A _Keenan Pepper_, Nov 30 2007
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