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A066281
Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 4.
8
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.
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
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