

A186705


The maximum number of occurrences of the same distance among n points in the plane.


1



0, 1, 3, 5, 7, 9, 12, 14, 18, 20, 23, 27, 30, 33
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OFFSET

1,3


COMMENTS

Upper bound is floor(k n^(4/3)), A129011 if k near enough to 1.
a(21)=57.
a(27)=81 (Hamming 3,3 graph).  Ed Pegg Jr, Feb 02 2018


REFERENCES

P. Brass, W. O. J. Moser, J. Pach, Research Problems in Discrete Geometry, Springer (2005), p. 183


LINKS

Table of n, a(n) for n=1..14.
Ed Pegg Jr, Maximally Dense Unit Distance Graphs


EXAMPLE

a(4) = 5 because there is a unit distance graph with 4 vertices of an equilateral rhombus such that all but one of the six pairs of vertices are unit distance apart.


CROSSREFS

Sequence in context: A047932 A139130 A219087 * A072154 A204206 A080751
Adjacent sequences: A186702 A186703 A186704 * A186706 A186707 A186708


KEYWORD

nonn,hard,more,nice


AUTHOR

Michael Somos, Feb 25 2011


STATUS

approved



