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

Offset

2,3

Comments

a(n) is the denominator (in lowest terms) of the maximum of min(|x_i-x_j| + |y_i-y_j| + |z_i-z_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'' k-subset 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: A209421 A320435 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