OFFSET
0,4
COMMENTS
The count can be built constructively by listing all possible sum-free sets of partitions into collections containing {1, ..., n}. For n>1, iterate over the previous generation and insert n into each partition if the result is sum-free, and also append n to the end as its own partition. See Example.
LINKS
Ben Burns, C# program to generate counts
Eric Weisstein's World of Mathematics, Sum-Free Set
EXAMPLE
Where "|" is a partition divider, then:
a(1)=1, given by { 1 }.
a(2)=1, given by { 1|2 }.
a(3)=3, given by { 1,3|2 }, { 1|2,3 }, { 1|2|3 }.
a(4)=6, given by { 1,3|2|4 }, { 1,4|2,3 }, { 1|2,3|4 }, { 1,4|2|3 }, { 1|2|3,4 }, { 1|2|3|4 }.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Ben Burns, Jun 17 2017
STATUS
approved