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

2,2

Comments

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

Links

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

Example

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.

Crossrefs

Cf. A000332, A003136, A024610.

A108279 is the analog for squares on square grids.

Sequence in context: A006463 A237886 A212555 * A339573 A060655 A117490

Adjacent sequences: A328784 A328785 A328786 * A328788 A328789 A328790

Keyword

nonn

Author

Peter Kagey, Oct 27 2019

Status

approved