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# Problem 600

## Integer sided equiangular hexagons

Let $H$($n$) be the number of distinct integer sided equiangular convex hexagons with perimeter not exceeding $n$.
Hexagons are distinct if and only if they are not congruent.

You are given $H$(6)=1, $H$(12)=10, $H$(100)=31248.
Find $H$(55106).

Equiangular hexagons with perimeter not exceeding 12