Good luck. I have thought about this one in my spare time ever since I saw it...
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).