--description--

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

$$\begin{align} & T(1) = 16 \\ & T(2) = 104 \end{align}$$

Find $T(36)$.

--hints--

crossHatchedTriangles() should return 343047.

assert.strictEqual(crossHatchedTriangles(), 343047);

--seed--

--seed-contents--

function crossHatchedTriangles() {

  return true;
}

crossHatchedTriangles();

--solutions--

// solution required