How many equilateral triangles are there in an eight-fold triangular grid. I was able to determine the number of 1x1, 2x2, 3x3, 4x4, 5x5, 6x6, 7x7, and 8x8 size triangles to be 64, 43, 27, 16, 10, 3, 1 respectively and the total number of triangles to be 170. I am having a hard time though coming up with a general formula to show for example how many 4x4 triangles are in a nine-fold triangle. I thought it had something to do with triangular numbers, but the pattern doesn't hold. Thanks for any help you can provide!!