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A001116 Maximal kissing number of an n-dimensional lattice.
(Formerly M1585 N0617)
3
0, 2, 6, 12, 24, 40, 72, 126, 240, 272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(9) = 272 was determined by Watson (1971). a(10) is probably 336.

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. p. 15.

J. Leech and N. J. A. Sloane, New sphere packings in dimensions 9-15, Bull. Amer. Math. Soc., 76 (1970), 1006-1010.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.

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

Watson, G. L., The number of minimum points of a positive quadratic form, Dissertationes Math., 84 (1971), 42 pp.

LINKS

Table of n, a(n) for n=0..9.

G. Nebe and N. J. A. Sloane, Table of highest kissing numbers known

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

N. J. A. Sloane, Seven Staggering Sequences.

Eric Weisstein's World of Mathematics, Kissing Number.

EXAMPLE

In three dimensions, each sphere in the face-centered cubic lattice D_3 touches 12 others, and the kissing number in any other three-dimensional lattice is less than 12.

CROSSREFS

Cf. A002336, A028923.

Sequence in context: A211978 A028923 A187272 * A002336 A030625 A029929

Adjacent sequences:  A001113 A001114 A001115 * A001117 A001118 A001119

KEYWORD

nonn,nice,hard,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

Lower bounds for the next 4 terms are 336, 438, 756, 918

STATUS

approved

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Last modified October 20 09:00 EDT 2014. Contains 248329 sequences.