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

1,7

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.

Links

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

Formula

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

Crossrefs

See A000162, A066281, A066283, A066287, A066288, A066453, A066454.

Sequence in context: A200008 A086751 A048281 * A028650 A028634 A170773

Adjacent sequences: A066270 A066271 A066272 * A066274 A066275 A066276

Keyword

nonn,more

Author

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

Extensions

Name clarified by John Mason, Sep 04 2024

More terms from John Mason, Sep 18 2024

Status

approved