A228881 Minimum number of spheres touching a wall of the container in the densest packing of n equal spheres into a cube.

1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 10, 10, 13, 14, 14, 13, 16, 17, 12, 14, 8, 12, 20, 15, 19, 20, 26, 22, 25, 26, 27, 28, 22

Offset: 1

Author

Hugo Pfoertner, Sep 13 2013

Keywords

• nonn
• more

Comments

Spheres that are not part of the rigid framework, "rattlers", are always assumed not to touch the walls of the container cube.

If optimal configurations can be obtained by taking away an arbitrary sphere from a configuration with a higher sphere count, a sphere touching the container wall is chosen.

Examples

			The first configuration in which there is an inner sphere not touching the walls occurs for n = 9, with 8 spheres in the corners of the cube and one sphere in the center of the cube. Therefore a(9) = 8.
		

Links

• Hugo Pfoertner, Densest Packing of Spheres in a Cube (Java Visualization)
• Eckard Specht, The best known packings of equal spheres in a cube, (complete up to N = 1000). [The title should be "The best packings known ..."! - _N. J. A. Sloane_, Mar 23 2021]

Crossrefs

Cf. A084824.

Extensions

a(25)-a(33) from Hugo Pfoertner, Mar 23 2021