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A323273
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Number of orbits of the Conway group Co_0 acting on vectors of norm 2n in the Leech lattice.
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1
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1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 2, 6, 3, 5, 5, 7
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OFFSET
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0,7
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REFERENCES
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J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985, p. 181. There is a typo in the table: the second line for vectors of type 11 should read u_3 + 2 v_4 (w_3).
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. Tables 4.13 and 4.14.
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LINKS
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EXAMPLE
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a(2) = 1 since the group acts transitively on the 196560 minimal vectors (which have norm 4).
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CROSSREFS
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A008408 gives the total number of vectors of norm 2n in the Leech lattice.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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