A320449 - OEIS

A320449

Number of antichains of sets whose multiset union is an integer partition of n.

1, 1, 2, 4, 6, 9, 18, 24, 39, 58, 92, 131, 206

(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(7) = 24 antichains:

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

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

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

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

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

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

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

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

{{1},{5}} {{1,2,4}}

{{2},{4}} {{1},{6}}

{{3},{3}} {{2},{5}}

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

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

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

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

{{1,2},{1,2}} {{1},{1},{5}}

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

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

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

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

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

{{1},{1},{1},{1},{1},{1}} {{1},{1},{1},{4}}

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

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

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

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

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

{{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]]]];

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@@@#, antiQ[#]]&]], {n, 10}]

CROSSREFS

Cf. A001970, A089259, A258466, A319719, A319721, A320328, A320353, A320355, A320356.

Sequence in context: A244470 A098787 A164138 * A263434 A192079 A079143

Adjacent sequences: A320446 A320447 A320448 * A320450 A320451 A320452

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 12 2018

STATUS

approved