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A320328

Number of square multiset partitions of integer partitions of n.

1, 1, 2, 3, 6, 11, 20, 36, 65, 117, 214, 382, 679 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`A multiset partition is square if its length is equal to its number of distinct atoms.`
	LINKS	`Table of n, a(n) for n=0..12.`
	EXAMPLE	`The a(1) = 1 through a(6) = 20 square partitions:` `{{1}} {{2}} {{3}} {{4}} {{5}} {{6}}` `{{1,1}} {{1,1,1}} {{2,2}} {{1},{4}} {{3,3}}` `{{1},{2}} {{1},{3}} {{2},{3}} {{1},{5}}` `{{1,1,1,1}} {{1},{1,3}} {{2,2,2}}` `{{1},{1,2}} {{1},{2,2}} {{2},{4}}` `{{2},{1,1}} {{2},{1,2}} {{1},{1,4}}` `{{3},{1,1}} {{4},{1,1}}` `{{1,1,1,1,1}} {{1},{1,1,3}}` `{{1},{1,1,2}} {{1,1},{1,3}}` `{{1,1},{1,2}} {{1},{1,2,2}}` `{{2},{1,1,1}} {{1,1},{2,2}}` `{{1,2},{1,2}}` `{{1},{2},{3}}` `{{2},{1,1,2}}` `{{3},{1,1,1}}` `{{1,1,1,1,1,1}}` `{{1},{1,1,1,2}}` `{{1,1},{1,1,2}}` `{{1,2},{1,1,1}}` `{{2},{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]]]];` `Table[Length[Select[Join@@mps/@IntegerPartitions[n], Length[#]==Length[Union@@#]&]], {n, 8}]`
	CROSSREFS	`Cf. A000219, A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A316983, A319066, A319312, A319616, A320330, A320331.` `Sequence in context: A002985 A239342 A093608 * A079976 A017992 A018172` `Adjacent sequences: A320325 A320326 A320327 * A320329 A320330 A320331`
	KEYWORD	`nonn,more`
	AUTHOR	`Gus Wiseman, Oct 11 2018`
	STATUS	`approved`

Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)