OFFSET
0,3
COMMENTS
A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem. The weight of an atom is 1, while the weight of a multiset is the sum of weights of its elements.
EXAMPLE
Non-isomorphic representatives of the a(2) = 2 through a(4) = 20 multisystems:
{1,1} {{1},{1,1}} {{{1}},{{1},{1,1}}}
{1,2} {{1},{1,2}} {{{1,1}},{{1},{1}}}
{{1},{2,3}} {{{1}},{{1},{1,2}}}
{{2},{1,1}} {{{1,1}},{{1},{2}}}
{{{1}},{{1},{2,2}}}
{{{1,1}},{{2},{2}}}
{{{1}},{{1},{2,3}}}
{{{1,1}},{{2},{3}}}
{{{1}},{{2},{1,1}}}
{{{1,2}},{{1},{1}}}
{{{1}},{{2},{1,2}}}
{{{1,2}},{{1},{2}}}
{{{1}},{{2},{1,3}}}
{{{1,2}},{{1},{3}}}
{{{1}},{{2},{3,4}}}
{{{1,2}},{{3},{4}}}
{{{2}},{{1},{1,1}}}
{{{2}},{{1},{1,3}}}
{{{2}},{{3},{1,1}}}
{{{2,3}},{{1},{1}}}
CROSSREFS
The non-maximal version is A330474.
The case where the leaves are sets (as opposed to multisets) is A330677.
The case with all atoms distinct is A000111.
The case with all atoms equal is (also) A000111.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 27 2019
STATUS
approved