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

1,4

Comments

Higher sequence terms are only conjectures found by numerical experimentation.

Links

Table of n, a(n) for n=1..34.

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.

Example

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.

Crossrefs

Cf. A084825, A084826, A084827, A084616.

Sequence in context: A280057 A257174 A327625 * A344710 A184615 A151969

Adjacent sequences: A084821 A084822 A084823 * A084825 A084826 A084827

Keyword

hard,more,nonn

Author

Hugo Pfoertner, Jun 12 2003

Extensions

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

Status

approved