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A319079 Number of connected antichains of sets whose multiset union is an integer partition of n. 2
1, 1, 2, 3, 4, 4, 8, 7, 12, 15, 19, 26, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

EXAMPLE

The a(10) = 19 clutters:

  {{10}}

  {{1,9}}

  {{2,8}}

  {{3,7}}

  {{4,6}}

  {{1,2,7}}

  {{1,3,6}}

  {{1,4,5}}

  {{2,3,5}}

  {{1,2,3,4}}

  {{5},{5}}

  {{1,2},{1,6}}

  {{1,2},{2,5}}

  {{1,3},{1,5}}

  {{1,4},{1,4}}

  {{2,3},{2,3}}

  {{1,2},{1,2},{1,3}}

  {{2},{2},{2},{2},{2}}

  {{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]]]]]]]]];

submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]];

antiQ[s_]:=Select[Tuples[s, 2], And[UnsameQ@@#, submultisetQ@@#]&]=={};

Table[Length[Select[Join@@mps/@IntegerPartitions[n], And[And@@UnsameQ@@@#, Length[csm[#]]==1, antiQ[#]]&]], {n, 10}]

CROSSREFS

Cf. A001970, A007718, A048143, A056156, A089259, A319719, A320351, A320353, A320355, A320356.

Sequence in context: A047966 A317085 A236543 * A325329 A224038 A241037

Adjacent sequences:  A319076 A319077 A319078 * A319080 A319081 A319082

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 12 2018

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)