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Hexagonal orchards

Problem 351

Published on 17 September 2011 at 10:00 pm [Server Time]

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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