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600. Integer sided equiangular hexagons

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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

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