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

0,4

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.

Links

Table of n, a(n) for n=0..6.

Example

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.

Sequence in context: A359222 A309417 A215654 * A209094 A293574 A322644

Adjacent sequences: A330674 A330675 A330676 * A330678 A330679 A330680

Keyword

nonn,more

Author

Gus Wiseman, Dec 30 2019

Status

approved