OFFSET
1,2
COMMENTS
For purposes of computing further terms, note that it suffices to consider multisets S having at most n-1 elements.
LINKS
Sean A. Irvine, Java program (github)
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gabriel D. Carroll (gastropodc(AT)hotmail.com), Jan 13 2001
EXTENSIONS
a(13)-a(15) from Sean A. Irvine, Sep 07 2022
STATUS
approved