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Number of set partitions of [n] such that each subset is sum-free.
1

%I #14 Jul 12 2017 08:55:04

%S 1,1,1,3,6,20,67,291,1099,5780,26249,153238,832366,5443440,32738738,

%T 239515824,1591963864,12548347149,93066370414

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

%C 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.

%H Ben Burns, <a href="/A288817/a288817.cs.txt">C# program to generate counts</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Sum-FreeSet.html">Sum-Free Set</a>

%e Where "|" is a partition divider, then:

%e a(1)=1, given by { 1 }.

%e a(2)=1, given by { 1|2 }.

%e a(3)=3, given by { 1,3|2 }, { 1|2,3 }, { 1|2|3 }.

%e 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 }.

%Y Cf. A007865, A000041.

%K nonn,more

%O 0,4

%A _Ben Burns_, Jun 17 2017