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A064705
Maximal number of vectors u_1, u_2, ... in R^n with |u_i| = 1 and |u_i - u_j| >= 1 for i, j distinct, where || is L1-norm.
0
1, 2, 8, 18, 40
OFFSET
0,2
COMMENTS
L1 norm of (a,b,c,...) = |a|+|b|+|c|+...
A lower bound if n = 2^m >= 4: a(n) >= 2n^2 + Sum_{r=2..[log_2 n]} A(2^r,2^(r-1))*A(n,2^r,2^r); compare the Edel-Rains-Sloane paper and the tables of And and Andw mentioned here - N. J. A. Sloane, Oct 12 2001. This gives 40 in 4-D, 256 in 8-D (found also by Blokhuis), 2144 in 16-D, etc.
LINKS
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128, Elect. J. Combin.
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128
EXAMPLE
It is easier to take the norm to be 2. For n=2: { +-2 0, 0 +-2, +-1 +-1 }; for n=3: { 200 etc. (6) and 110 etc. (12) }; for n=4: { 2000 etc. (8), 1100 etc. (24), .5 .5 .5 .5 etc. (8) }.
CROSSREFS
Sequence in context: A198014 A252592 A188577 * A377676 A220909 A376192
KEYWORD
nonn,more
AUTHOR
Aart Blokhuis (aartb(AT)win.tue.nl), Oct 11 2001
STATUS
approved