A066454 Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 2.

0, 0, 1, 4, 10, 34, 71, 246, 522, 1783, 3765, 12858, 27496, 94525, 203318, 702789, 1522315, 5290592, 11519095, 40214441, 87947507, 308236670

Offset: 1

Author

Brendan Owen (brendan_owen(AT)yahoo.com), Dec 27 2001

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

Cf. A000162, A066453, A066273, A066281, A066283, A066287, A066288.

Formula

a(n) = 2*B(n)+2*C(n)+J(n)+BE(n)+BF(n)+CE(n)+CK(n)+EE(n), see Lunnon paper for naming convention. - John Mason, Sep 18 2024

Extensions

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