--description--

A hexagonal orchard of order $n$ is a triangular lattice made up of points within a regular hexagon with side $n$. The following is an example of a hexagonal orchard of order 5:

Highlighted in green are the points which are hidden from the center by a point closer to it. It can be seen that for a hexagonal orchard of order 5, 30 points are hidden from the center.

Let $H(n)$ be the number of points hidden from the center in a hexagonal orchard of order $n$.

$H(5) = 30$. $H(10) = 138$. $H(1\,000)$ = $1\,177\,848$.

Find $H(100\,000\,000)$.

--hints--

hexagonalOrchards() should return 11762187201804552.

assert.strictEqual(hexagonalOrchards(), 11762187201804552);

--seed--

--seed-contents--

function hexagonalOrchards() {

  return true;
}

hexagonalOrchards();

--solutions--

// solution required