A084824 Maximum number of spheres of diameter one that can be packed in a cube of volume n (i.e., with edge length n^(1/3)).

1, 1, 1, 2, 4, 4, 5, 8, 8, 8, 9, 9, 10, 11, 14, 14, 14, 15, 18, 18, 19, 19, 21, 21, 23, 24, 27, 27, 27, 27, 32, 32, 32, 33

Offset: 1

Author

Hugo Pfoertner, Jun 12 2003

Keywords

• hard
• more
• nonn

Comments

Higher sequence terms are only conjectures found by numerical experimentation.

Examples

			a(5) = 4 because a cube of edge length 5^(1/3) = 1.7099759 is large enough to contain 4 spheres arranged as a tetrahedron, which requires a minimum enclosing cube of edge length 1+sqrt(2)/2 = 1.70710678.
		

Links

• Dave Boll, Optimal Packing of Circles and Spheres
• Thierry Gensane, Dense Packings of Equal Spheres in a Cube, The Electronic Journal of Combinatorics 11 (2004), #R33.
• M. Goldberg, On the Densest Packing of Equal Spheres in a Cube, Math. Mag. 44, 199-208, 1971.
• Hugo Pfoertner, Best packing of equal spheres in a cube. Numerical results.
• Hugo Pfoertner, Densest Packings of Equal Spheres in a Cube. Visualizations.
• J. Schaer, On the Densest Packing of Spheres in a Cube, Can. Math. Bul. 9, 265-270, 1966.

Crossrefs

Cf. A084825, A084826, A084827, A084616.

Extensions

Corrected erroneous a(14) and extended to a(34) by Hugo Pfoertner, including results from Thierry Gensane, Jun 23 2011