  Consider the set $\{1,2,\ldots,3n\}$. We are interested in the number of
partitions of this set into subsets of three elements each, where the sum of
two of them equals the third.
  We give some criteria such a partition has to fulfill, which can be used for
efficient pruning in the search for these partitions. In particular, we
enumerate all such partitions for $n=16$ and $n=17$ adding new terms to the
series A108235 in the Online Encyclopedia of Integer Sequences.
