A066287 Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 8.

0, 1, 1, 2, 2, 1, 1, 2, 4, 2, 5, 7, 8, 5, 10, 17, 20, 12, 23, 42, 48, 30, 59, 108

Offset: 1

Author

Brendan Owen (brendan_owen(AT)yahoo.com), Jan 01 2002

Keywords

• nonn

Comments

The entry a(14)=2 does not match the examples in A000162, which propose a(14)=5. - R. J. Mathar, Sep 03 2024

The sequence counts "one-sided" polycubes (A000162); chiral polycubes count twice. - John Mason, Sep 04 2024

References

• W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.

Crossrefs

See A000162, A066273, A066281, A066283, A066288, A066453, A066454.

Formula

a(n) = 2*AB(n)+BBC(n), see Lunnon paper for naming convention. - John Mason, Sep 04 2024

Extensions

a(14) corrected (after comment from R. J. Mathar), a(15)-a(24) added, and name clarified by John Mason, Sep 04 2024