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A296994
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.
0
1, 3, 4, 7, 10, 14, 18, 20, 23, 27, 31, 36, 42, 48, 54, 61, 68, 76, 84, 92, 98
OFFSET
1,2
COMMENTS
This sequence generalizes the idea of A003002 ("no 3-term arithmetic progressions") for triangular point grids.
For the same idea applied to square grids see A296468 and A300131.
EXAMPLE
At most 54 points (X) can be chosen from a 15 X 15 X 15 triangular point grid under the condition mentioned above. Example:
o
X X
X o X
o X X o
X X o X X
X o o o o X
o o X o X o o
o o o o o o o o
o o X X o X X o o
o X o o X X o o X o
X X o o X o X o o X X
X o X X o o o o X X o X
o X X o o X o X o o X X o
X X o X X o o o o X X o X X
X o o o o X X o X X o o o o X
CROSSREFS
Sequence in context: A287410 A228643 A304066 * A382046 A236475 A287458
KEYWORD
nonn,nice,hard,more
AUTHOR
Heinrich Ludwig, Mar 26 2018
EXTENSIONS
a(20) from Heinrich Ludwig, Apr 24 2018
a(21) from Heinrich Ludwig, May 01 2018
STATUS
approved