A272385 Number of polycubes with n cells, allowing vertex connections and edge connections as well as face connections, distinguishing mirror images.

1, 3, 16, 246, 4866, 115520, 2873712, 73884172, 1941259395

Offset: 1

Author

George Sicherman, Apr 28 2016

Keywords

• nonn
• more
• nice
• hard

Examples

			For n=2 there are three possibilities: the two cubes share a face, or only an edge, or only a vertex.
For n=3, there are 14 tricubes allowing vertex, edge, and face connections. Two of them have distinct mirror images, so a(3) = 16.
		

Crossrefs

Cf. A272368 (identifying mirror images), A270862 (no vertex connections), A000162 (face connections only).

Extensions

a(8) and a(9) from Joerg Arndt, Dec 13 2023