%I M2060 #45 Oct 06 2023 07:33:02

%S 1,2,13,73,710,6079,85308

%N Number of arithmetic n-dimensional crystal classes.

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

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

%D 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.

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

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

%H Akinari Hoshi, Ming-chang Kang and Aiichi Yamasaki, <a href="https://doi.org/10.1090/memo/1403">Multiplicative Invariant Fields of Dimension <= 6</a>, Memoirs of the AMS, 2023.

%H W. Plesken and T. Schulz, Dominik Bernhardt and others, <a href="https://lbfm-rwth.github.io/carat/">Computer package CARAT</a>

%H W. Plesken and T. Schulz, <a href="http://wwwb.math.rwth-aachen.de/carat/">CARAT Homepage</a> [dead link]

%H W. Plesken and T. Schulz, <a href="/A006226/a006226.pdf">CARAT Homepage</a> [Cached copy in pdf format (without subsidiary pages), with permission]

%H W. Plesken and T. Schulz, <a href="/A006226/a006226_1.pdf">Introduction to CARAT</a> [Cached copy in pdf format (without subsidiary pages), with permission]

%H W. Plesken and T. Schulz, <a href="http://projecteuclid.org/euclid.em/1045604675">Counting crystallographic groups in low dimensions</a>, Experimental Mathematics, 9 (No. 3, 2000), 407-411.

%H R. L. E. Schwarzenberger, <a href="https://doi.org/10.1112/blms/16.3.209">Colour symmetry</a>, Bulletin of the London Mathematical Society 16.3 (1984): 216-229.

%Y Cf. A004028, A004029, A006227, A307288.

%K nonn,hard,nice,more

%O 0,2

%A _N. J. A. Sloane_

%E a(6) corrected from CARAT page by _D. S. McNeil_, Jan 02 2011