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%I #13 Dec 13 2023 03:49:45
%S 1,3,16,246,4866,115520,2873712,73884172,1941259395
%N Number of polycubes with n cells, allowing vertex connections and edge connections as well as face connections, distinguishing mirror images.
%e For n=2 there are three possibilities: the two cubes share a face, or only an edge, or only a vertex.
%e For n=3, there are 14 tricubes allowing vertex, edge, and face connections. Two of them have distinct mirror images, so a(3) = 16.
%Y Cf. A272368 (identifying mirror images), A270862 (no vertex connections), A000162 (face connections only).
%K nonn,more,nice,hard
%O 1,2
%A _George Sicherman_, Apr 28 2016
%E a(8) and a(9) from _Joerg Arndt_, Dec 13 2023
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