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Integer sided equiangular hexagons

Problem 600 Published on Saturday, 22nd April 2017, 04:00 pm; Solved by 422;
Difficulty rating: 35%

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).

p600-equiangular-hexagons.png

Equiangular hexagons with perimeter not exceeding 12