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

Offset

2,1

Comments

a(n) is the numerator (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?

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