

A054909


Number of 8ndimensional even unimodular lattice (or quadratic forms).


6




OFFSET

0,3


COMMENTS

King shows that a(4) >= 1162109024.  Charles R Greathouse IV, Nov 05 2013


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, p. 49.


LINKS

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. 839863.
Steven R. Finch, MinkowskiSiegel mass constants [Broken link]
Steven R. Finch, MinkowskiSiegel mass constants


CROSSREFS

Cf. A005134, A054907, A054908, A054911.
Sequence in context: A162605 A118812 A228241 * A171636 A270562 A100816
Adjacent sequences: A054906 A054907 A054908 * A054910 A054911 A054912


KEYWORD

nonn,nice,hard


AUTHOR

N. J. A. Sloane, May 23 2000


EXTENSIONS

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)


STATUS

approved



