A268666
Number of polycubes with n cells, allowing edge connections as well as face connections, identifying mirror images.
Original entry on oeis.org
1, 2, 8, 64, 646, 9364, 151028, 2605148, 46350675
Offset: 1
a(2) = 2 because there are two ways to join two cells in the cubic grid at faces or edges.
A272385
Number of polycubes with n cells, allowing vertex connections and edge connections as well as face connections, distinguishing mirror images.
Original entry on oeis.org
1, 3, 16, 246, 4866, 115520, 2873712, 73884172, 1941259395
Offset: 1
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.
Cf.
A272368 (identifying mirror images),
A270862 (no vertex connections),
A000162 (face connections only).
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