Problem 351

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).





已知H(5) = 30,H(10) = 138,H(1 000) = 1177848。

求H(100 000 000).