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A001116
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Maximal kissing number of an n-dimensional lattice.
(Formerly M1585 N0617)
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7
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OFFSET
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0,2
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COMMENTS
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a(9) = 272 was determined by Watson (1971). a(10) is probably 336.
Lower bounds for the next 4 terms are 336, 438, 756, 918.
Trivial upper bounds given by A257479 are 553, 869, 1356, 2066.
a(n) coincides with A257479(n) when a lattice achieves the non-lattice-constrained kissing number, for a(0)=0, a(1)=2, a(2)=6 (A_2), a(3)=12 (A_3), a(4)=24 (D_4), a(8)=240 (E_8) and a(24)=196560 (Leech). A002336(n) agrees with a(n) for all n<=9 (and equality is unknown thereafter), and A028923(n)=a(n) iff n<=6. (End)
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. p. 15.
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).
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LINKS
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FORMULA
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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STATUS
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approved
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