A288817 Number of set partitions of [n] such that each subset is sum-free.

1, 1, 1, 3, 6, 20, 67, 291, 1099, 5780, 26249, 153238, 832366, 5443440, 32738738, 239515824, 1591963864, 12548347149, 93066370414

Offset: 0

Author

Ben Burns, Jun 17 2017

Keywords

• nonn
• more

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.

Examples

			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 }.
		

Links

• Ben Burns, C# program to generate counts
• Eric Weisstein's World of Mathematics, Sum-Free Set

Crossrefs

Cf. A007865, A000041.