A131628 Maximal size of an n-distance set in the plane.

1, 3, 5, 7, 9, 12, 13

Offset

0,2

Comments

A set of points in the plane is called an n-distance set if there are precisely n different distances between pairs of distinct points.

A186704(a(n)) = n and a(n) is the maximum value for which this is true. - Michael Somos, Feb 25 2011

Links

Table of n, a(n) for n=0..6.

J. H. Conway and N. J. A. Sloane, Lattices with Few Distances, J. Number Theory, 39 (1991), pp. 75-90 [a related paper]

P. Erdos and P. Fishburn, Maximum planar sets that determine k distances, Discrete Math. 160 (1996), 115-125.

M. Shinohara, Uniqueness of maximum planar five-distance sets, Discrete Math., 308 (2008), 3048-3055.

N. J. A. Sloane, The unique 12-point 5-distance configuration [A poor sketch - ignore the double lines!]

Wei Xianglin, A Proof of Erdos-Fishburn's Conjecture for g(6)=13, Electronic J. Combinatorics, 19 (2012), #P38. - From N. J. A. Sloane, Dec 05 2012

Example

a(n) = 2*n + 1 for n = 0 to 4 which comes from the 2*n + 1 vertices of a regular polygon.

Crossrefs

Sequence in context: A356750 A083964 A340439 * A079091 A353149 A191749

Adjacent sequences: A131625 A131626 A131627 * A131629 A131630 A131631

Keyword

nonn,more

Author

N. J. A. Sloane, May 29 2008

Status

approved