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A300131
Largest number of points that can be placed on an n X n point grid so that no point is equally distant from two other points on the same straight line.
2
1, 4, 6, 9, 16, 17, 21, 26, 31, 34, 40, 46
OFFSET
1,2
COMMENTS
This definition is a 2-dimensional generalization of A003002 ("no 3-term arithmetic progressions"). It generalizes the definition of A296468 to include not only triples on horizontal or vertical lines but on any straight line.
EXAMPLE
On a 10 X 10 point grid 34 points (X) can be placed at most. Example:
. X . . . X X . . .
X X . . . X X . X .
X . X X . . . . X .
. . X . . . . X . X
. . . . . . . . X X
X X . . . . . . . .
X . X . . . . X . .
. X . . . . X X . X
. X . X X . . . X X
. . . X X . . . X .
CROSSREFS
Sequence in context: A115665 A118694 A085648 * A045114 A010436 A085955
KEYWORD
nonn,hard,more
AUTHOR
Heinrich Ludwig, Feb 26 2018
EXTENSIONS
a(11) from Bert Dobbelaere, Jan 09 2020
a(12) from Bert Dobbelaere, Jan 12 2020
STATUS
approved