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%I #4 Oct 04 2012 10:28:59
%S 4,6,4,2,10,12,14,2,4,2,6,2,4,1,2,2,2,12,2,2,1
%N Conjectured order of the symmetry group of the (numerically computed) least-perimeter cluster of n nonoverlapping circles.
%C This can be thought of as the order of the symmetry group of the minimum-energy configuration of n two-dimensional bubbles in a plane. a(1) is infinite, because one bubble forms a circle, which has a continuous symmetry group containing rotations of arbitrary angles. So far, the actual symmetry groups are all dihedral, except for a(15) and a(22), which are trivial (their configurations have no symmetries).
%D Cox, S. J., F. Graner, M. F. Vaz, C. Monnereau-Pittet and N. Pittet, 2003, Minimal perimeter for N identical bubbles in two dimensions: calculations and simulations, Philos. Mag. 83, 1393-1406.
%D F. Morgan, Soap bubble clusters, Rev. Mod. Phys. Vol. 79 (2007), pp. 821-827.
%H R. L. Graham and N. J. A. Sloane, <a href="http://neilsloane.com/doc/RLG/138.pdf">Penny-Packing and Two-Dimensional Codes</a>, Discrete and Comput. Geom. 5 (1990), 1-11.
%e a(3) = 6 because three planar bubbles arrange themselves in an equilateral-triangle-type configuration with symmetry group D_3, of order 6.
%Y Cf. A133491.
%K nonn
%O 2,1
%A _Keenan Pepper_, Dec 27 2007
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