login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317078 Number of connected multiset partitions of strongly normal multisets of size n. 7
1, 1, 3, 6, 18, 46, 172, 563, 2347 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.
LINKS
EXAMPLE
The a(3) = 6 connected multiset partitions are (111), (1)(11), (1)(1)(1), (112), (1)(12), (123).
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], multijoin@@s[[c[[1]]]]]]]]];
strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];
Length/@Table[Join@@Table[Select[mps[m], Length[csm[#]]==1&], {m, strnorm[n]}], {n, 8}]
CROSSREFS
Sequence in context: A032120 A115344 A223044 * A289587 A151262 A148555
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 20 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)