1,2

For purposes of computing further terms, note that it suffices to consider multisets S having at most n-1 elements.

Consider n = 3; then the multiset {0} has 0 as the sum of any subset; {1} has a subset with sum 0 (the empty set) and one with sum 1; {2} has one with sum 0 and one with sum 2; {1,1} has sums 0, 1 and 2 represented. Thus {0}, {0,1}, {0,2}, {0,1,2} are possible values for the set of subset sums (mod 3). Conversely, any S has a subset whose sum is 0 (viz. the empty set), so these are all the possible sets of subset sums; there are 4 of them.

Note that n = 6 is the smallest value for which there exists a subset of Z/nZ, containing 0, which is not a set of subset sums.

Sequence in context: A045844 A063108 A161140 this_sequence A130917 A007612 A112395

Adjacent sequences: A058958 A058959 A058960 this_sequence A058962 A058963 A058964

nonn

Gabriel D. Carroll (gastropodc(AT)hotmail.com), Jan 13 2001