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A320351 Number of connected multiset partitions of integer partitions of n. 4
1, 1, 3, 5, 11, 18, 38, 66, 130, 237, 449, 823, 1538 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..12.

EXAMPLE

The a(1) = 1 through a(5) = 18 multiset partitions:

  {{1}}  {{2}}      {{3}}          {{4}}              {{5}}

         {{1,1}}    {{1,2}}        {{1,3}}            {{1,4}}

         {{1},{1}}  {{1,1,1}}      {{2,2}}            {{2,3}}

                    {{1},{1,1}}    {{1,1,2}}          {{1,1,3}}

                    {{1},{1},{1}}  {{2},{2}}          {{1,2,2}}

                                   {{1,1,1,1}}        {{1,1,1,2}}

                                   {{1},{1,2}}        {{1},{1,3}}

                                   {{1},{1,1,1}}      {{2},{1,2}}

                                   {{1,1},{1,1}}      {{1,1,1,1,1}}

                                   {{1},{1},{1,1}}    {{1},{1,1,2}}

                                   {{1},{1},{1},{1}}  {{1,1},{1,2}}

                                                      {{1},{1,1,1,1}}

                                                      {{1,1},{1,1,1}}

                                                      {{1},{1},{1,2}}

                                                      {{1},{1},{1,1,1}}

                                                      {{1},{1,1},{1,1}}

                                                      {{1},{1},{1},{1,1}}

                                                      {{1},{1},{1},{1},{1}}

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]]], Union@@s[[c[[1]]]]]]]]];

Table[Length[Select[Join@@mps/@IntegerPartitions[n], Length[csm[#]]==1&]], {n, 8}]

CROSSREFS

Cf. A001970, A007718, A048143, A056156, A258466, A261006, A293994, A319719, A320328, A320330, A320331, A320355, A320356.

Sequence in context: A320789 A269628 A162891 * A319641 A306895 A198519

Adjacent sequences:  A320348 A320349 A320350 * A320352 A320353 A320354

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 11 2018

STATUS

approved

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)