I am trying to calculate how many triangles that can be found in an equilateral triangle with $2n$ lines starting at the bottom angles and ending at the opposite side, such that equally many lines start/end of either side.
This is rather hard to explain, so I drew that first 5 terms:
The 1st term has, of course, 1 triangle.
The 2nd term has 8 triangles.
The 3rd term has 27 triangles.
This problem is really killing me, so any help would be greatly appreciated.