A084826 Best packing of m>1 equal spheres in a cube setting a new density record.

2, 3, 4, 6, 7, 8, 31, 32, 48, 60, 61, 62, 63

Offset

1,1

Comments

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.

References

See under A084824.

Links

Table of n, a(n) for n=1..13.

Dave Boll, Packing spheres in cubes

Hugo Pfoertner, Best packing of equal spheres in a cube. Numerical results.

Hugo Pfoertner, Densest packing of 32 spheres in a cube. Video.

Hugo Pfoertner, Densest packing of 48 spheres in a cube. Video.

Hugo Pfoertner, Densest packing of 63 spheres in a cube. Video.

Crossrefs

Cf. A084824, A084829, A051657.

Sequence in context: A138936 A135604 A345437 * A118944 A132988 A363997

Adjacent sequences: A084823 A084824 A084825 * A084827 A084828 A084829

Keyword

hard,more,nonn

Author

Hugo Pfoertner, Jun 12 2003

Extensions

More terms from Hugo Pfoertner, Oct 03 2015

Status

approved