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A248866
Discrete Heilbronn Triangle Problem: a(n) is twice the maximal area of the smallest triangle defined by three vertices that are a subset of n points on an n X n square lattice.
2
4, 9, 6, 6, 5, 6, 5, 6, 6, 6, 6
OFFSET
3,1
COMMENTS
For n points in an n X n square, find the three points that make the triangle with minimal area. a(n) is double the maximal area of this triangle.
It is conjectured that the sequence has an infinite repetition of only two integers.
EXAMPLE
a(3) = 4 because 3 points can be chosen so the minimal triangle has area 2:
.x.
...
x.x
a(6) = 6 because 3 points can be chosen so the minimal triangle has area 3:
..x..x
......
x.....
.....x
......
x..x..
a(8) is greater than or equal to 4 because of this non-optimal arrangement:
.....x.x
........
x.x.....
........
........
x.x.....
........
.....x.x
a(8) = 6 because 3 points can be chosen so the minimal triangle has area 3:
..x..x..
........
x......x
........
........
x......x
........
..x..x..
CROSSREFS
Sequence in context: A108533 A200414 A347215 * A168608 A200383 A199513
KEYWORD
nonn,more
AUTHOR
Gordon Hamilton, Mar 04 2015
EXTENSIONS
a(5), a(7) and a(9) corrected and a(10)-a(13) added by Hiroaki Yamanouchi, Mar 09 2015
STATUS
approved