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%I #6 Sep 07 2022 18:18:21
%S 1,2,4,8,16,22,50,65,108,163,282,343,601,781,1205
%N Number of possible sets {sum(T) : T contained in S}, where S is a multiset of elements of Z/nZ.
%C For purposes of computing further terms, note that it suffices to consider multisets S having at most n-1 elements.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a058/A058961.java">Java program</a> (github)
%e 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.
%e 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.
%K nonn,more
%O 1,2
%A Gabriel D. Carroll (gastropodc(AT)hotmail.com), Jan 13 2001
%E a(13)-a(15) from _Sean A. Irvine_, Sep 07 2022