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A330474 Number of non-isomorphic balanced reduced multisystems of weight n. 16
1, 1, 2, 7, 48, 424 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
EXAMPLE
Non-isomorphic representatives of the a(3) = 7 multisystems:
{1,1,1}
{1,1,2}
{1,2,3}
{{1},{1,1}}
{{1},{1,2}}
{{1},{2,3}}
{{2},{1,1}}
Non-isomorphic representatives of the a(4) = 48 multisystems:
{1,1,1,1} {{1},{1,1,1}} {{{1}},{{1},{1,1}}}
{1,1,1,2} {{1,1},{1,1}} {{{1,1}},{{1},{1}}}
{1,1,2,2} {{1},{1,1,2}} {{{1}},{{1},{1,2}}}
{1,1,2,3} {{1,1},{1,2}} {{{1,1}},{{1},{2}}}
{1,2,3,4} {{1},{1,2,2}} {{{1}},{{1},{2,2}}}
{{1,1},{2,2}} {{{1,1}},{{2},{2}}}
{{1},{1,2,3}} {{{1}},{{1},{2,3}}}
{{1,1},{2,3}} {{{1,1}},{{2},{3}}}
{{1,2},{1,2}} {{{1}},{{2},{1,1}}}
{{1,2},{1,3}} {{{1,2}},{{1},{1}}}
{{1},{2,3,4}} {{{1}},{{2},{1,2}}}
{{1,2},{3,4}} {{{1,2}},{{1},{2}}}
{{2},{1,1,1}} {{{1}},{{2},{1,3}}}
{{2},{1,1,3}} {{{1,2}},{{1},{3}}}
{{1},{1},{1,1}} {{{1}},{{2},{3,4}}}
{{1},{1},{1,2}} {{{1,2}},{{3},{4}}}
{{1},{1},{2,2}} {{{2}},{{1},{1,1}}}
{{1},{1},{2,3}} {{{2}},{{1},{1,3}}}
{{1},{2},{1,1}} {{{2}},{{3},{1,1}}}
{{1},{2},{1,2}} {{{2,3}},{{1},{1}}}
{{1},{2},{1,3}}
{{1},{2},{3,4}}
{{2},{3},{1,1}}
CROSSREFS
Labeled versions are A330475 (strongly normal) and A330655 (normal).
The case where the atoms are all different is A318813.
The case where the atoms are all equal is (also) A318813.
The labeled case of set partitions is A005121.
The labeled case of integer partitions is A330679.
The case of maximal depth is A330663.
The version where leaves are sets (as opposed to multisets) is A330668.
Sequence in context: A341214 A106159 A160915 * A277501 A277503 A317666
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 26 2019
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)