A292444 Number of non-isomorphic finite multisets that cannot be expressed as the multiset-union of a set of sets.

0, 1, 1, 2, 3, 5, 6, 9, 12, 17, 22, 30, 39, 50, 65, 83, 105, 131, 167, 207, 257, 317, 391, 478, 585, 708, 864, 1037, 1252, 1498

Offset: 1

Author

Gus Wiseman, Oct 02 2017

Keywords

• nonn
• more

Comments

Non-isomorphic finite multisets correspond to integer partitions. For example, the partition (3221) corresponds to the multiset {1,1,1,2,2,3,3,4}.

Examples

			Representatives of the a(7) = 6 multisets are: {1,1,1,1,1,1,1}, {1,1,1,1,1,1,2}, {1,1,1,1,1,2,2}, {1,1,1,1,1,2,3}, {1,1,1,1,2,2,2}, {1,1,1,1,2,2,3}.
		

Crossrefs

Cf. A049311, A089259, A116540, A283877, A292432.

Extensions

a(12)-a(30) from Bert Dobbelaere, Mar 30 2025