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A317077 Number of connected multiset partitions of normal multisets of size n. 8
1, 1, 3, 8, 28, 110, 519, 2749, 16317 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A multiset is normal if it spans an initial interval of positive integers.

LINKS

Table of n, a(n) for n=0..8.

EXAMPLE

The a(3) = 8 connected multiset partitions are (111), (1)(11), (1)(1)(1), (122), (2)(12), (112), (1)(12), (123).

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

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

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

CROSSREFS

Cf. A007716, A007718, A048143, A293994, A303837, A303838, A304716, A305078.

Cf. A317073, A317075, A317078, A317079, A317080.

Sequence in context: A093356 A224271 A135583 * A009437 A000776 A327030

Adjacent sequences:  A317074 A317075 A317076 * A317078 A317079 A317080

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 20 2018

STATUS

approved

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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)