A345206 Maximum number of unit cubes that can be fully enclosed in n unit cubes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 20, 20, 22, 22, 24, 24, 27

Offset: 8

Author

Abraham Maxfield, Jun 11 2021

Keywords

• nonn

Comments

Cubes are assumed to be aligned in a 3D grid. Cubes with an exposed edge or corner are not considered enclosed.

The Moore neighborhood of a cube in a 3-D grid consists of the 26 that share a face, an edge, or a vertex with it. - N. J. A. Sloane, Jul 12 2021

Examples

			a(26) = 1 as the number of neighbors in Moore's neighborhood is 26 in 3D.
		

Crossrefs

Cf. A345205. 3D equivalent to A008642.