Problem 251

Cardano Triplets

A triplet of positive integers (`a`,`b`,`c`) is called a Cardano Triplet if it satisfies the condition:

For example, (2,1,5) is a Cardano Triplet.

There exist 149 Cardano Triplets for which `a`+`b`+`c` 1000.

Find how many Cardano Triplets exist such that `a`+`b`+`c` 110,000,000.

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