A328787 Number of distinct sizes of equilateral triangles with vertices in an equilateral triangular array of points with n rows.

1, 2, 4, 6, 8, 11, 14, 17, 21, 25, 28, 33, 38, 43, 49, 54, 59, 66, 73, 80, 87, 93, 100, 109, 116, 124, 133, 142, 150, 161, 172, 181, 191, 201, 211, 224, 234, 246, 258, 271, 282, 295, 307, 319, 333, 346, 359, 375, 389, 403, 420, 435, 448, 465, 482, 499, 514

Offset: 2

Author

Peter Kagey, Oct 27 2019

Keywords

• nonn

Comments

a(n) <= A024610(n-1) - 1.

Examples

			For n = 4, the a(4) = 4 sizes of equilateral triangles are 1, sqrt(3), 2, and 3. For example,
     *         o         *              *
    * *       * o       o o            o o
   o o o     o o *     * o *          o o o
  o o o o,  o * o o,  o o o o,  and  * o o *.
For n = 7, the a(7) = 11 equilateral triangles have side lengths 1, sqrt(3), 2, sqrt(7), 3, sqrt(12), sqrt(13), 4, sqrt(21), 5, and 6.
		

Links

• Peter Kagey, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000332, A003136, A024610.

A108279 is the analog for squares on square grids.