## Integer sided equiangular hexagons

### Problem 600

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*