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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 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..21.


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


                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


Cf. A296468, A300131.

Sequence in context: A287410 A228643 A304066 * A236475 A287458 A050572

Adjacent sequences:  A296991 A296992 A296993 * A296995 A296996 A296997




Heinrich Ludwig, Mar 26 2018


a(20) from Heinrich Ludwig, Apr 24 2018

a(21) from Heinrich Ludwig, May 01 2018



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Last modified October 22 18:05 EDT 2019. Contains 328319 sequences. (Running on oeis4.)