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Number of 3-dimensional polyominoes (or polycubes) with n cells that have cavities (inclusions of empty space).
2

%I #28 Oct 29 2022 08:22:21

%S 20,404,6164,75917,835491

%N Number of 3-dimensional polyominoes (or polycubes) with n cells that have cavities (inclusions of empty space).

%C Even if two polycubes are mirror images of each other, they are considered different for this sequence.

%C Polycubes with less than 11 cells can't have cavities.

%C Largest enclosed volume >= A355880(n-5) for polycubes with n cells.

%H Gleb Ivanov, <a href="/A355966/a355966.py.txt">Python program for n = 11..14</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polycube">Polycube</a>

%Y Cf. A001419, A000162, A038119, A355880.

%Y Cf. A357083 (without distinguished reflections).

%K nonn,more,hard

%O 11,1

%A _Gleb Ivanov_, Jul 21 2022