# Problem 351: Hexagonal orchards

![graphic](img351.gif)

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) =
1177848. Find H(100 000 000).