Efficient Calculation the Number of Partitions of the Set $\{1,2,\dots ,3n\}$ into Subsets $\{x,y,z\}$ Satisfying $x+y=z$

Christian Hercher, Frank Niedermeyer

Consider the set $\{1,2,\dots ,3n\}$. 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.…