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Integer sided equiangular hexagons

Published on Saturday, 22nd April 2017, 04:00 pm; Solved by 472;
Difficulty rating: 35%

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).

p600-equiangular-hexagons.png

Equiangular hexagons with perimeter not exceeding 12