You mean straight alkanes, for the odd/even difference, don't you? You might want to check if there's any density difference between them.
Melting points are extremely complicated, possibly unaccessible to simple reasoning and only to heavy software estimation. Working theories don't exist, additive models (Joback and few more) fail with 100K error. It's presently a research topic, with some limited success, where software is to try many possible packings of molecules - remember the orientation and overlap of molecules in a crystal isn't known a priori, nor the periodicity, and even the molecule conformation may adapt to the best crystal. Worse: many organic compounds have allotropes.
Symmetry of the molecule is very important, beyond packing possibilities. Symmetric cubane, adamantane, 2,2,3,3-tetramethyl-butane... have very high melting points close to their boiling point. Symmetry favours the solid since a free "liquid" molecule has better chances to stick to the crystal; check the odd/even n-alkane story with this.
Ease of rotations and vibrations at the "liquid" molecule favours the liquid, since these degrees of freedom use to be hampered at the solid. One more argument for cubane and adamantane. Branched alkanes also rotate more easily and gem-branched less so, which would be compatible with tendencies in the melting point - but easy packing is a very convincing reason as well.
Mankind would need a good means to estimate melting points. Up to now, we have additive methods that fail, and very (very) few measurements - maybe too few to build a theory or software on them. Most Internet data is software estimation, off by >100K, without warning. The Yaws is a heavy book filled by such faulty software, completely wrong, beware. So if you want to discover or invent this means, welcome! Be it a theory, a method, a light or more probably a medium-heavy (=PC) software, I don't care.