Sacrieur -- Just doing f(20) is 22926606 comparisons.
Sacrieur -- Unless you have a super computer, I don't see you doing that.
Sacrieur -- THEN you have to take all of your sequences and compare them ALL, counting only one of each prefix family.
Sacrieur -- If you were brute forcing it, you would start with i = 1 and iterate through all Collatz sequences starting with i, throwing out the ones that don't have a length of 90.
Sacrieur -- Here's the thing though, the prefix families aren't even given to you, you have to come up with a way to generate the families on your own.
Sacrieur -- f(20) = 6771 means that for a Collatz Sequence as described, there are 6771 distinct prefix families. That's 6771 prefix families that, if you had to brute force, you had to check against each of the other ones.