A066281 - OEIS

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

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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

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

KEYWORD

nonn,more,changed

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