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A004027 Number of arithmetic n-dimensional crystal classes.
(Formerly M2060)
8
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.

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.

Sequence in context: A163190 A242991 A240549 * A263840 A154357 A161130

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 June 25 00:43 EDT 2016. Contains 274191 sequences.