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A121269 Number of maximal sum-free subsets of {1,2,...,n}.

%I A121269 #26 May 10 2025 14:39:56
%S A121269 1,1,2,2,4,5,6,8,13,17,23,29,37,51,66,86,118,158,201,265,359,471,598,
%T A121269 797,1043,1378,1765,2311,3064,3970,5017,6537,8547,11020,14007,18026,
%U A121269 23404,30026,37989,48945,62759,80256,101070,129193,164835,209279,262693,334127
%N A121269 Number of maximal sum-free subsets of {1,2,...,n}.
%C A121269 Also the number of maximal subsets of {1..n} containing no differences of pairs of elements. - _Gus Wiseman_, Jul 10 2019
%H A121269 Fausto A. C. Cariboni, <a href="/A121269/b121269.txt">Table of n, a(n) for n = 0..80</a>
%H A121269 P. J. Cameron and P. Erdős, <a href="https://www.researchgate.net/publication/247043302_On_the_number_of_sets_of_integers_with_various_properties">On the number of integers with various properties</a>, in R. A. Mullin, ed., Number Theory: Proc. First Conf. of Canad. Number Theory Assoc. Conf., Banff, De Gruyter, Berlin, 1990, pp. 61-79.
%H A121269 N. Hindman and H. Jordan, <a href="http://nyjm.albany.edu/j/2007/13-6.html">Measures of sum-free intersecting families</a>, New York J. Math. 13 (2007), 97-106.
%e A121269 a(5)=5 because the maximal sum-free subsets of {1,2,3,4,5} are {1,4}, {2,3}, {2,5}, {1,3,5} and {3,4,5}
%e A121269 From _Gus Wiseman_, Jul 10 2019: (Start)
%e A121269 The a(1) = 1 through a(8) = 13 subsets:
%e A121269   {1}  {1}  {1,3}  {1,3}  {1,4}    {2,3}    {1,4,6}    {1,3,8}
%e A121269        {2}  {2,3}  {1,4}  {2,3}    {1,3,5}  {1,4,7}    {1,4,6}
%e A121269                    {2,3}  {2,5}    {1,4,6}  {2,3,7}    {1,4,7}
%e A121269                    {3,4}  {1,3,5}  {2,5,6}  {2,5,6}    {1,5,8}
%e A121269                           {3,4,5}  {3,4,5}  {2,6,7}    {1,6,8}
%e A121269                                    {4,5,6}  {3,4,5}    {2,5,6}
%e A121269                                             {1,3,5,7}  {2,5,8}
%e A121269                                             {4,5,6,7}  {2,6,7}
%e A121269                                                        {3,4,5}
%e A121269                                                        {1,3,5,7}
%e A121269                                                        {2,3,7,8}
%e A121269                                                        {4,5,6,7}
%e A121269                                                        {5,6,7,8}
%e A121269 (End)
%t A121269 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A121269 Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Plus@@@Tuples[#,2]]=={}&]]],{n,0,10}] (* _Gus Wiseman_, Jul 10 2019 *)
%Y A121269 Maximal product-free subsets are A326496.
%Y A121269 Sum-free subsets are A007865.
%Y A121269 Maximal sum-free and product-free subsets are A326497.
%Y A121269 Subsets with sums are A326083.
%Y A121269 Maximal subsets without sums of distinct elements are A326498.
%Y A121269 Cf. A103580, A326020, A326489, A326495.
%K A121269 nonn
%O A121269 0,3
%A A121269 N. Hindman (nhindman(AT)aol.com), Aug 23 2006
%E A121269 a(0) = 1 prepended by _Gus Wiseman_, Jul 10 2019
%E A121269 Terms a(42) and beyond from _Fausto A. C. Cariboni_, Oct 26 2020