Efficient calculation of the number of partitions of the set {1,2,…,3n} into subsets {x,y,z} satisfying x+y=z

Abstract

Consider the set [Formula: see text]. We are interested in determining the number of partitions of this set into subsets of three elements each, where the sum of two of the elements equals the third. To achieve this, we provide a set of criteria that must be met by any valid partition. These criteria then can be used for efficient pruning in the search for these partitions. Specifically, we enumerate all such partitions for [Formula: see text] and [Formula: see text], and added these new terms to the series A108235 in the Online Encyclopedia of Integer Sequences.