A330677 Number of non-isomorphic balanced reduced multisystems of weight n and maximum depth whose leaves (which are multisets of atoms) are sets.

1, 1, 1, 2, 11, 81, 859

Offset: 0

Author

Gus Wiseman, Dec 30 2019

Keywords

• nonn
• more

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.

Examples

			Non-isomorphic representatives of the a(0) = 1 through a(4) = 11 multisystems:
  {}  {1}  {1,2}  {{1},{1,2}}  {{{1}},{{1},{1,2}}}
                  {{1},{2,3}}  {{{1}},{{1},{2,3}}}
                               {{{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},{1,3}}}
                               {{{2,3}},{{1},{1}}}
		

Crossrefs

The version with all distinct atoms is A000111.

Non-isomorphic set multipartitions are A049311.

The (non-maximal) tree version is A330626.

Allowing leaves to be multisets gives A330663.

The case with prescribed degrees is A330664.

The version allowing all depths is A330668.

Cf. A000669, A001678, A004114, A005121, A007716, A141268, A283877, A306186, A330465, A330470, A330624.