A058961 Number of possible sets {sum(T) : T contained in S}, where S is a multiset of elements of Z/nZ.

1, 2, 4, 8, 16, 22, 50, 65, 108, 163, 282, 343, 601, 781, 1205

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

Table of n, a(n) for n=1..15.

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

Sequence in context: A257350 A257165 A262224 * A130917 A007612 A112395

Adjacent sequences: A058958 A058959 A058960 * A058962 A058963 A058964

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