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A317776 Number of strict multiset partitions of normal multisets of size n, where a multiset is normal if it spans an initial interval of positive integers. 6
1, 3, 13, 59, 313, 1847, 11977 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

The a(3) = 13 strict multiset partitions:

  {{1,1,1}}, {{1},{1,1}},

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

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

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

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]]]];

allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];

Table[Length[Select[Join@@mps/@allnorm[n], UnsameQ@@#&]], {n, 9}]

CROSSREFS

Cf. A001055, A007716, A045778, A255906, A281116, A317449, A317532, A317583, A317653, A317752, A317757, A317775.

Sequence in context: A151232 A151233 A151234 * A145942 A074437 A026578

Adjacent sequences:  A317773 A317774 A317775 * A317777 A317778 A317779

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2018

STATUS

approved

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Last modified April 19 16:18 EDT 2019. Contains 322282 sequences. (Running on oeis4.)