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A004027 Number of arithmetic n-dimensional crystal classes.
(Formerly M2060)
9
1, 2, 13, 73, 710, 6079, 85308 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of Z-classes of finite subgroups of GL_n(Z) up to conjugacy.

REFERENCES

H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.

P. Engel, Geometric crystallography, in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.

R. L. E. Schwarzenberger, N-Dimensional Crystallography. Pitman, London, 1980, p. 34.

Schwarzenberger, R. L. E. "Colour symmetry." Bulletin of the London Mathematical Society 16.3 (1984): 216-229.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..6.

W. Plesken and T. Schulz, CARAT Homepage

W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]

W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]

W. Plesken and T. Schulz, Counting crystallographic groups in low dimensions, Experimental Mathematics, 9 (No. 3, 2000), 407-411.

CROSSREFS

Cf. A004029, A006227, A307288.

Sequence in context: A163190 A242991 A240549 * A263840 A307288 A154357

Adjacent sequences:  A004024 A004025 A004026 * A004028 A004029 A004030

KEYWORD

nonn,hard,nice,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(6) corrected from CARAT page by D. S. McNeil, Jan 02 2011

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)