A066281 Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 4.

0, 0, 0, 0, 0, 3, 5, 11, 11, 24, 35, 84, 92, 174, 254, 606, 658, 1255, 1769, 4353, 4667, 9131

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

The sequence counts "one-sided" polycubes (A000162); chiral polycubes count twice. - John Mason, Sep 18 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, A066283, A066287, A066288, A066453, A066454.

Formula

a(n) = 2*A(n)+2*BB(n)+2*BC(n)+AE(n)+BFF(n)+CJ(n)+EEE(n)+EF(n)+EFF(n), see Lunnon paper for naming convention. - John Mason, Sep 18 2024

Extensions

Name clarified and more terms from John Mason, Sep 18 2024