A225973 Number of union-closed partitions of weight n.

1, 1, 1, 2, 3, 5, 6, 9, 12, 16, 22, 30, 39, 52, 67, 84, 112, 140, 176, 220, 282, 336, 434, 527, 660, 798, 998, 1186, 1480, 1767, 2165, 2586, 3168, 3732, 4556, 5389, 6482, 7654, 9211, 10789, 12937, 15153, 18037, 21086, 25060, 29159, 34527, 40172, 47301, 54927

Offset

0,4

Comments

The objects being counted are sets of sets of positive integers; each such set is closed under set union, and the sum of all the elements of its elements is n.

The sequence is related to Frankl's notorious union-closed sets conjecture, see the Wikipedia link.

References

This sequence was proposed by David S. Newman, in a note to the SeqFan mailing list, dated May 19 2013.

Links

Table of n, a(n) for n=0..49.

Wikipedia, Union-closed sets conjecture

David S. Newman, Need help calculating

Example

For n = 5, the a(5) = 5 union-closed partitions are: {{5}}, {{4,1}}, {{3,2}}, {{3,1},{1}}, {{2,1},{2}}.
{{3},{2}} has the correct sum, but is not closed under union.

Crossrefs

Cf. A050342 (answers a similar question without the requirement that the sets be closed under union).

Sequence in context: A067593 A084993 A046966 * A329165 A292444 A035948

Adjacent sequences: A225970 A225971 A225972 * A225974 A225975 A225976

Keyword

nonn

Author

Allan C. Wechsler, May 26 2013

Status

approved