_{This problem is a programming version of Problem 163 from projecteuler.net}

Consider an equilateral triangle in which straight lines are drawn from each vertex to the middle of the opposite side, such as in the size 1 triangle in the sketch below.

Sixteen triangles of either different shape or size or orientation or location can now be observed in that triangle. Using size 1 triangles as building blocks, larger triangles can be formed, such as the size 2 triangle in the above sketch. One-hundred and four triangles of either different shape or size or orientation or location can now be observed in that size 2 triangle.

It can be observed that the size 2 triangle contains size 1 triangle building blocks. A size 3 triangle would contain size 1 triangle building blocks and a size n triangle would thus contain size 1 triangle building blocks.

If we denote as the number of triangles present in a triangle of size , then

You are given . Find .