(Translated by https://www.hiragana.jp/)
A004028 - OEIS
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A004028
Number of geometric n-dimensional crystal classes.
(Formerly M1965)
9
1, 2, 10, 32, 227, 955, 7103
OFFSET
0,2
COMMENTS
Number of Q-classes of finite subgroups of GL_n(Z) up to conjugacy.
Number of n-dimensional crystallographic point groups (not counting enantiomorphs). - Andrey Zabolotskiy, Jul 08 2017
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.
T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 73.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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.
E. S. Rosenthal & N. J. A. Sloane, Correspondence, 1975.
CROSSREFS
Sequence in context: A264960 A151019 A329427 * A263839 A236921 A316644
KEYWORD
nonn,hard,nice,more
EXTENSIONS
a(6) corrected from CARAT page by D. S. McNeil, Jan 02 2011
STATUS
approved