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A225973 Number of union-closed partitions of weight n. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 25 23:08 EST 2020. Contains 331270 sequences. (Running on oeis4.)