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

1,4

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.

Links

Table of n, a(n) for n=1..24.

Formula

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

Crossrefs

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

Sequence in context: A209805 A238453 A376991 * A059260 A239473 A135229

Adjacent sequences: A066284 A066285 A066286 * A066288 A066289 A066290

Keyword

nonn

Author

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

Extensions

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

Status

approved