

A225973


Number of unionclosed 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 unionclosed 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, Unionclosed sets conjecture
David S. Newman, Need help calculating


EXAMPLE

For n = 5, the a(5) = 5 unionclosed 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



