%I #34 May 02 2019 08:15:31

%S 1,3,4,7,10,14,18,20,23,27,31,36,42,48,54,61,68,76,84,92,98

%N Largest number of points that can be selected from an n X n X n triangular point grid so that no selected point is equally distant from two other selected points on a straight line, which is parallel to one side of the grid.

%C This sequence generalizes the idea of A003002 ("no 3-term arithmetic progressions") for triangular point grids.

%C For the same idea applied to square grids see A296468 and A300131.

%e At most 54 points (X) can be chosen from a 15 X 15 X 15 triangular point grid under the condition mentioned above. Example:

%e o

%e X X

%e X o X

%e o X X o

%e X X o X X

%e X o o o o X

%e o o X o X o o

%e o o o o o o o o

%e o o X X o X X o o

%e o X o o X X o o X o

%e X X o o X o X o o X X

%e X o X X o o o o X X o X

%e o X X o o X o X o o X X o

%e X X o X X o o o o X X o X X

%e X o o o o X X o X X o o o o X

%Y Cf. A296468, A300131.

%K nonn,nice,hard,more

%O 1,2

%A _Heinrich Ludwig_, Mar 26 2018

%E a(20) from _Heinrich Ludwig_, Apr 24 2018

%E a(21) from _Heinrich Ludwig_, May 01 2018