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A066454
Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 2.
8
0, 0, 1, 4, 10, 34, 71, 246, 522, 1783, 3765, 12858, 27496, 94525, 203318, 702789, 1522315, 5290592, 11519095, 40214441, 87947507, 308236670
OFFSET
1,4
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*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
KEYWORD
nonn,more
AUTHOR
Brendan Owen (brendan_owen(AT)yahoo.com), Dec 27 2001
EXTENSIONS
Name clarified and more terms from John Mason, Sep 18 2024
STATUS
approved