A007361 Numerator of n-th power of Hermite constant for dimension n. (Formerly M3201)

1, 4, 2, 4, 8, 64, 64, 256

Offset

1,2

Comments

From the work of Cohn and Kumar we know that a(24) = 4^24 = 281474976710656.

References

Iskander Aliev, On the lattice programming gap of the group problems, Operations Research Letters 43 (2015) 199-202

J. W. S. Cassels, An Introduction to the Geometry of Numbers. Springer-Verlag, NY, 2nd ed., 1971, p. 332.

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 20.

P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers, North-Holland, Amsterdam, 2nd ed., 1987, p. 410.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..8.

H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices, arXiv:math/0403263 [math.MG], 2004-2017.

H. Cohn and A. Kumar, The densest lattice in twenty-four dimensions, arXiv:math/0408174 [math.MG], 2004.

Eric Weisstein's World of Mathematics, Hermite Constants.

Example

1, 4/3, 2, 4, 8, 64/3, 64, 256, ... = A007361/A007362.

Crossrefs

Cf. A007362.

Sequence in context: A016693 A345413 A137718 * A128136 A048147 A203001

Adjacent sequences: A007358 A007359 A007360 * A007362 A007363 A007364

Keyword

nonn,hard,nice,frac,more

Author

N. J. A. Sloane

Status

approved