Transitive relations on a set of n elements

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How to find out the total number of transitive relations in a set of n elements? I am facing a problem in finding all the possible cases, is it not possible to find all cases? If not possible, why?

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Wikipedia claims that no general formula that counts transitive relations is known.

Of course, for any particular $n$ you can just find all of them by brute force, but that may take a lot of effort even for smallish $n$s -- even for four elements there are thousands of possible transitive relations.