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A317757 Number of non-isomorphic multiset partitions of size n such that the blocks have empty intersection. 35
0, 1, 4, 17, 56, 205, 690, 2446, 8506, 30429 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

Non-isomorphic representatives of the a(4) = 17 multiset partitions:

  {1}{234},{2}{111},{2}{113},{11}{22},{11}{23},{12}{34},

  {1}{1}{22},{1}{1}{23},{1}{2}{11},{1}{2}{12},{1}{2}{13},{1}{2}{34},{2}{3}{11},

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

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]]]];

strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];

sysnorm[m_]:=If[Union@@m!=Range[Max@@Flatten[m]], sysnorm[m/.Rule@@@Table[{(Union@@m)[[i]], i}, {i, Length[Union@@m]}]], First[Sort[sysnorm[m, 1]]]]; sysnorm[m_, aft_]:=If[Length[Union@@m]<=aft, {m}, With[{mx=Table[Count[m, i, {2}], {i, Select[Union@@m, #>=aft&]}]}, Union@@(sysnorm[#, aft+1]&/@Union[Table[Map[Sort, m/.{par+aft-1->aft, aft->par+aft-1}, {0, 1}], {par, First/@Position[mx, Max[mx]]}]])]];

Table[Length[Union[sysnorm/@Join@@Table[Select[mps[m], Intersection@@#=={}&], {m, strnorm[n]}]]], {n, 6}]

CROSSREFS

Cf. A007716, A035310, A255906, A281116, A317073, A317533.

Cf. A317748, A317751, A317752, A317755.

Cf. A319077, A319748, A319755, A319778, A319781, A319790.

Sequence in context: A255526 A264218 A121327 * A183924 A255271 A293798

Adjacent sequences:  A317754 A317755 A317756 * A317758 A317759 A317760

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2018

EXTENSIONS

a(8) - a(10) from Gus Wiseman, Sep 27 2018

STATUS

approved

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Last modified May 23 20:23 EDT 2019. Contains 323528 sequences. (Running on oeis4.)