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%I #13 Oct 17 2015 10:39:48
%S 2,3,4,6,7,8,31,32,48,60,61,62,63
%N Best packing of m>1 equal spheres in a cube setting a new density record.
%C The terms >=31 are only conjectures found by numerical experimentation. In the table given at the Pfoertner link, the densities are given relative to the density of the cubic lattice packing (Pi/6). The first known arrangement with higher density than that of the cubic lattice packing was found for m=31 spheres. In the region 8<m<27 increasing packing densities occur for m=9,13,14. m=14 comes very close (0.994949) to the cubic lattice packing density.
%D See under A084824.
%H Dave Boll, <a href="http://web.archive.org/web/20140228175551/http://home.comcast.net/~davejanelle/packing.html">Packing spheres in cubes</a>
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a084824.txt">Best packing of equal spheres in a cube. Numerical results.</a>
%H Hugo Pfoertner, <a href="https://www.youtube.com/watch?v=lmVvo_84Zvo">Densest packing of 32 spheres in a cube.</a> Video.
%H Hugo Pfoertner, <a href="https://www.youtube.com/watch?v=-bsvKUzKsoc">Densest packing of 48 spheres in a cube.</a> Video.
%H Hugo Pfoertner, <a href="https://www.youtube.com/watch?v=yUuP6uvWPVA">Densest packing of 63 spheres in a cube.</a> Video.
%Y Cf. A084824, A084829, A051657.
%K hard,more,nonn
%O 1,1
%A _Hugo Pfoertner_, Jun 12 2003
%E More terms from _Hugo Pfoertner_, Oct 03 2015