A345205 -id:A345205 - cp's OEIS frontend

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

Abraham Maxfield, Jun 11 2021

nonn

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

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

Cf. A345205. 3D equivalent to A008642.

A373927 a(n) is the minimum number of hypercubes needed to admit a hole of size n in the 4D tesseractic honeycomb.

Original entry on oeis.org

16, 80, 106, 132

Offset: 0

Abraham Maxfield, Jun 22 2024

			16 hypercubes surround a single vertex so a(0) = 16.
A 3 X 3 X 3 X 3 hypercube will admit a single hole in its center, so a(1) = 3*3*3*3 - 1 = 80.

Cf. A345205 (3D equivalent), A235382 (2D equivalent).

cp's OEIS Frontend

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

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