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A054909 Number of 8n-dimensional even unimodular lattice (or quadratic forms). 6
1, 1, 2, 24 (list; graph; refs; listen; history; text; internal format)
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", Springer-Verlag, 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. 839-863.

S. R. Finch, Minkowski-Siegel 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

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Last modified February 24 11:12 EST 2018. Contains 299603 sequences. (Running on oeis4.)