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Maximum number of unit cubes that can be fully enclosed in n unit cubes.
1

%I #19 Jul 12 2021 16:28:40

%S 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,

%T 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,

%U 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

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

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

%C 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

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

%Y Cf. A345205. 3D equivalent to A008642.

%K nonn

%O 8,27

%A _Abraham Maxfield_, Jun 11 2021