  The combinatorics of tilings of a hexagon of integer side-length $n$ by 120
degree - 60 degree diamonds of side-length 1 has a long history, both directly
(as a problem of interest in thermodynamic models) and indirectly (through the
equivalence to plane partitions). Formulae as products of factorials have been
conjectured and, one by one, proven for the number of such tilings under each
of the symmetries of the hexagon. However, when this note was written the entry
for the number of distinct such tilings in the Online Encyclopedia of Integer
Sequences (OEIS) consisted of little more than a table for $0 \le n \le 4$ and
a brief discussion of those values. The aim of this note is to pull together
the relevant facts.
