A292432 Number of normal multisets that cannot be expressed as the multiset-union of a set of sets.

0, 1, 1, 3, 5, 9, 16, 27, 46, 76, 130, 203, 350, 554, 890, 1474, 2285, 3732, 5852, 9297, 14628, 22936, 35903, 55893, 86967, 134585, 207934, 321122, 492634, 757490

Offset: 1

Author

Gus Wiseman, Oct 02 2017

Keywords

• nonn
• more

Comments

A multiset is normal if it spans an initial interval of positive integers. Most normal multisets can be expressed as the multiset-union of a set of sets. For example, {1,1,2,2} is the multiset-union of {{1},{2},{1,2}}.

Examples

			The a(6) = 9 multisets are: {1,1,1,1,1,1}, {1,1,1,1,1,2}, {1,1,1,1,2,2}, {1,1,1,1,2,3}, {1,1,1,2,2,2}, {1,1,2,2,2,2}, {1,2,2,2,2,2}, {1,2,2,2,2,3}, {1,2,3,3,3,3}.
		

Crossrefs

Cf. A049311, A089259, A116540, A283877, A292444.

Extensions

a(11)-a(30) from Bert Dobbelaere, Mar 30 2025