If I count the first triangle there is 1

If I count the triangles in the second triangle there are 4 triangles plus 1 (original)

If I count the triangles in the third triangle there are 12 triangles plus 1 (original).

If I extend the pattern then, the general formula appears to be .

n levels	number of triangles
1	1
2	5
3	13
4	27

For proof use triangular numbers.