You say "practical values of n", but the answer to n = 27 is already known and I would be very surprised if the final result had any practical application. The

You say "practical values of n", but the answer to n = 27 is already known and I would be very surprised if the final result had any practical application. The point of these problems is rarely the numerical answer, but the development of new techniques: The problem of determining the asymptotic growth of this number is studied because it is a good playground for sharpening mathematical tools and methods. In this sense, the asymptotic problem is an interesting one, and it was solved. Now that the main term is characterized, people can investigate sharper estimates. The problem of determining an efficient algorithm for every n, on the other hand, is just hopeless, which means that it is not interesting for the purpose I described above. Studying "small" n (up to 40, say) is not useless, though, if it leads to algorithmic breakthroughs (in SAT solving, for example). It is, however, an "orthogonal" problem, in the sense that it requires a completely different set of techniques. To illustrate my point: If the answer for n = 50 appeared out of nowhere, would people care about the number itself? I bet people would be much more interested in how it was done.