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

1,2

Links

Table of n, a(n) for n=1..9.

Example

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).

Sequence in context: A000273 A071897 A182012 * A013923 A053466 A005031

Adjacent sequences: A272382 A272383 A272384 * A272386 A272387 A272388

Keyword

nonn,more,nice,hard

Author

George Sicherman, Apr 28 2016

Extensions

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

Status

approved