A066273 Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 3.

0, 0, 0, 1, 0, 0, 4, 0, 3, 24, 4, 18, 151, 25, 136, 992, 184, 938, 6769, 1300, 6792, 47469

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

This 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, A066281, A066283, A066287, A066288, A066453, A066454.

Formula

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

Extensions

Name clarified by John Mason, Sep 04 2024

More terms from John Mason, Sep 18 2024