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

1,6

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.

Links

Table of n, a(n) for n=1..22.

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

Crossrefs

See A000162, A066273, A066283, A066287, A066288, A066453, A066454.

Sequence in context: A071328 A273037 A006538 * A072063 A242269 A309426

Adjacent sequences: A066278 A066279 A066280 * A066282 A066283 A066284

Keyword

nonn,more

Author

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

Extensions

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

Status

approved