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

1,2

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.

Links

Table of n, a(n) for n=1..33.

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]

Example

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.

Crossrefs

Cf. A084824.

Sequence in context: A079631 A347623 A269849 * A252373 A245338 A160755

Adjacent sequences: A228878 A228879 A228880 * A228882 A228883 A228884

Keyword

nonn,more

Author

Hugo Pfoertner, Sep 13 2013

Extensions

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

Status

approved