cp's OEIS Frontend

A151897 Number of subsets of {1, 2, ..., n} such that no member is a sum of distinct other members.

%I A151897 #13 Apr 11 2021 08:00:45
%S A151897 1,2,4,7,13,22,37,60,100,155,249,381,591,889,1365,2009,3047,4453,6602,
%T A151897 9567,14151,20228,29654,42302,61369,87108,126066,177580,256039,360304,
%U A151897 515740,724069,1036860,1448746,2069526,2893311,4117725,5749540,8186555
%N A151897 Number of subsets of {1, 2, ..., n} such that no member is a sum of distinct other members.
%C A151897 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 A151897 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 A151897 Fausto A. C. Cariboni, <a href="/A151897/b151897.txt">Table of n, a(n) for n = 0..85</a>
%e A151897 a(4) = 13, including all subsets of {1, 2, 3, 4} except {1, 2, 3} (excluded
%e A151897 because 1+2 = 3), {1, 3, 4} (excluded because 1+3 = 4), and {1, 2, 3, 4} (excluded for both reasons.)
%e A151897 From _Gus Wiseman_, Jun 07 2019: (Start)
%e A151897 The a(0) = 1 through a(4) = 13 subsets:
%e A151897   {}  {}   {}     {}     {}
%e A151897       {1}  {1}    {1}    {1}
%e A151897            {2}    {2}    {2}
%e A151897            {1,2}  {3}    {3}
%e A151897                   {1,2}  {4}
%e A151897                   {1,3}  {1,2}
%e A151897                   {2,3}  {1,3}
%e A151897                          {1,4}
%e A151897                          {2,3}
%e A151897                          {2,4}
%e A151897                          {3,4}
%e A151897                          {1,2,4}
%e A151897                          {2,3,4}
%e A151897 (End)
%t A151897 Table[Length[Select[Subsets[Range[n]],Intersection[#,Plus@@@Subsets[#,{2,Length[#]}]]=={}&]],{n,0,10}] (* _Gus Wiseman_, Jun 07 2019 *)
%Y A151897 Cf. A007865, A050291, A085489, A103580, A308546, A326080, A326083, A326117.
%K A151897 nonn
%O A151897 0,2
%A A151897 _David Wasserman_, Apr 16 2008
%E A151897 a(0) = 1 prepended by _Gus Wiseman_, Jun 07 2019