login
A303546
Number of non-isomorphic aperiodic multiset partitions of weight n.
28
1, 3, 9, 29, 90, 285, 909, 2984, 9935, 34113, 119368, 428923, 1574223, 5915235, 22699730, 89000042, 356058539, 1453069854, 6044132793, 25612564200, 110503626702, 485161228675, 2166488899641, 9835209480533, 45370059225227
OFFSET
1,2
COMMENTS
A multiset is aperiodic if its multiplicities are relatively prime. For this sequence neither the parts nor their multiset union are required to be aperiodic, only the multiset of parts.
LINKS
FORMULA
a(n) = Sum_{d|n} mu(d) * A007716(n/d).
EXAMPLE
Non-isomorphic representatives of the a(3) = 9 aperiodic multiset partitions are:
{{1,1,1}}, {{1,2,2}}, {{1,2,3}},
{{1},{1,1}}, {{1},{2,2}}, {{1},{2,3}}, {{2},{1,2}},
{{1},{2},{2}}, {{1},{2},{3}}.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2018
STATUS
approved