

A243487


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


2



2, 2, 4, 1, 1, 4, 3, 2, 2, 3, 4, 8, 1, 1, 10, 6, 4, 4
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OFFSET

2,1


COMMENTS

a(n) is the numerator (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?


EXAMPLE

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


CROSSREFS

Denominator is A243576(n).
Sequence in context: A068450 A071436 A214741 * A143485 A181633 A245204
Adjacent sequences: A243484 A243485 A243486 * A243488 A243489 A243490


KEYWORD

nonn,frac


AUTHOR

Robert Israel, Jun 06 2014


EXTENSIONS

More terms from Robert Israel, Jun 22 2014


STATUS

approved



