Problem 163

Cross-hatched triangles

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 4 *size 1* triangle building blocks. A *size 3* triangle would contain 9 *size 1* triangle building blocks and a *size n* triangle would thus contain *n ^{2} size 1* triangle building blocks.

If we denote T(`n`) as the number of triangles present in a triangle of *size n*, then

T(1) = 16

T(2) = 104

Find T(36).

**
These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
**