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A007361 Numerator of n-th power of Hermite constant for dimension n.
(Formerly M3201)
+0
2
1, 4, 2, 4, 8, 64, 64, 256 (list; graph; listen)
OFFSET

1,2

REFERENCES

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

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.

LINKS

H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices

H. Cohn and A. Kumar, The densest lattice in twenty-four dimensions

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

EXAMPLE

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

CROSSREFS

Cf. A007362.

Sequence in context: A154793 A016693 A137718 this_sequence A128136 A048147 A051666

Adjacent sequences: A007358 A007359 A007360 this_sequence A007362 A007363 A007364

KEYWORD

nonn,hard,nice,frac

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

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

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.


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