Problem 351

Hexagonal orchards

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).

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These problems are part of
Project Euler
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