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Number of subsets of {1, 2, ..., n} such that no member is a sum of distinct other members.
70

%I #13 Apr 11 2021 08:00:45

%S 1,2,4,7,13,22,37,60,100,155,249,381,591,889,1365,2009,3047,4453,6602,

%T 9567,14151,20228,29654,42302,61369,87108,126066,177580,256039,360304,

%U 515740,724069,1036860,1448746,2069526,2893311,4117725,5749540,8186555

%N Number of subsets of {1, 2, ..., n} such that no member is a sum of distinct other members.

%C This sequence and A085489 first differ at n = 7. a(7) = 60, A085489(7) = 61. A085489(7) includes {1, 2, 4, 7}, which is excluded from a(7) because 1+2+4 = 7.

%C If this sequence counts sum-free sets, A326080 counts sum-closed sets, which are different from sum-full sets (A093971). - _Gus Wiseman_, Jun 07 2019

%H Fausto A. C. Cariboni, <a href="/A151897/b151897.txt">Table of n, a(n) for n = 0..85</a>

%e a(4) = 13, including all subsets of {1, 2, 3, 4} except {1, 2, 3} (excluded

%e because 1+2 = 3), {1, 3, 4} (excluded because 1+3 = 4), and {1, 2, 3, 4} (excluded for both reasons.)

%e From _Gus Wiseman_, Jun 07 2019: (Start)

%e The a(0) = 1 through a(4) = 13 subsets:

%e {} {} {} {} {}

%e {1} {1} {1} {1}

%e {2} {2} {2}

%e {1,2} {3} {3}

%e {1,2} {4}

%e {1,3} {1,2}

%e {2,3} {1,3}

%e {1,4}

%e {2,3}

%e {2,4}

%e {3,4}

%e {1,2,4}

%e {2,3,4}

%e (End)

%t Table[Length[Select[Subsets[Range[n]],Intersection[#,Plus@@@Subsets[#,{2,Length[#]}]]=={}&]],{n,0,10}] (* _Gus Wiseman_, Jun 07 2019 *)

%Y Cf. A007865, A050291, A085489, A103580, A308546, A326080, A326083, A326117.

%K nonn

%O 0,2

%A _David Wasserman_, Apr 16 2008

%E a(0) = 1 prepended by _Gus Wiseman_, Jun 07 2019