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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

%I #21 Jan 12 2020 14:04:09

%S 1,4,6,9,16,17,21,26,31,34,40,46

%N 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.

%C 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.

%e On a 10 X 10 point grid 34 points (X) can be placed at most. Example:

%e . X . . . X X . . .

%e X X . . . X X . X .

%e X . X X . . . . X .

%e . . X . . . . X . X

%e . . . . . . . . X X

%e X X . . . . . . . .

%e X . X . . . . X . .

%e . X . . . . X X . X

%e . X . X X . . . X X

%e . . . X X . . . X .

%Y Cf. A003002, A296468.

%K nonn,hard,more

%O 1,2

%A _Heinrich Ludwig_, Feb 26 2018

%E a(11) from _Bert Dobbelaere_, Jan 09 2020

%E a(12) from _Bert Dobbelaere_, Jan 12 2020