## Hexagonal orchards

### Problem 351

Published on Saturday, 17th September 2011, 10:00 pm; Solved by 1319; Difficulty rating: 25%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).