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 $n$.

$H(5)=30$. $H(10)=138$. $H(1000)=1177848$.

Find $H(100000000)$.