

A243576


Denominator of largest minimal l^1 distance for n points in the simplex x+y+z=1, 0<=x,y,z<=1.


1



1, 1, 3, 1, 1, 5, 4, 3, 3, 5, 7, 15, 2, 2, 21, 13, 9, 9
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OFFSET

2,3


COMMENTS

a(n) is the denominator (in lowest terms) of the maximum of min(x_ix_j + y_iy_j + z_iz_j, 1 <= i < j <= n) where x_i, y_i, z_i >= 0, x_i + y_i + z_i = 1 for 1<=i<=n.


LINKS

Table of n, a(n) for n=2..19.
Robert Israel, A packing problem
Robert Israel, A packing problem [Cached version, pdf format, with permission]
Robert Israel, Illustration for a(17), with caption
Robert Israel, Illustration for a(17), without caption
Math Overflow, What is the most ``diverse'' ksubset of [0,1]^m?


FORMULA

For n=3 an optimal configuration consists of [1,0,0],[0,1,0],[0,0,1], with all distances 2, so a(3) = 1.


CROSSREFS

Numerator is A243487(n).
Sequence in context: A026780 A209421 A275421 * A211314 A026703 A122917
Adjacent sequences: A243573 A243574 A243575 * A243577 A243578 A243579


KEYWORD

nonn,frac


AUTHOR

Robert Israel, Jun 06 2014


EXTENSIONS

More terms from Robert Israel, Jun 22 2014


STATUS

approved



