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A054909
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Number of 8n-dimensional even unimodular lattice (or quadratic forms).
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6
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OFFSET
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0,3
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COMMENTS
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King shows that a(4) >= 1162109024. - Charles R Greathouse IV, Nov 05 2013
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 49.
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LINKS
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Table of n, a(n) for n=0..3.
Oliver King, A mass formula for unimodular lattices with no roots, Mathematics of Computation 72:242 (2003), pp. 839-863.
Steven R. Finch, Minkowski-Siegel mass constants [Broken link]
Steven R. Finch, Minkowski-Siegel mass constants
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CROSSREFS
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Cf. A005134, A054907, A054908, A054911.
Sequence in context: A162605 A118812 A228241 * A171636 A270562 A100816
Adjacent sequences: A054906 A054907 A054908 * A054910 A054911 A054912
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KEYWORD
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nonn,nice,hard
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AUTHOR
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N. J. A. Sloane, May 23 2000
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EXTENSIONS
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The classical mass formula shows that the next term is at least 8*10^7.
Oliver King and Richard Borcherds (reb(AT)math.berkeley.edu) have recently improved this estimate and have shown that a(4), the number in dimension 32, is at least 10^9 (Jul 22 2000)
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STATUS
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approved
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