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A326498 Number of maximal subsets of {1..n} containing no sums of distinct elements.

%I A326498 #14 Oct 11 2020 03:10:32
%S A326498 1,1,1,3,3,6,11,16,20,32,53,78,107,149,206,292,391,556,782,1062,1451,
%T A326498 1929,2564,3404,4431,5853,7672,9999,12973,16922,22194,28655,36734,
%U A326498 47036,60375,76866,97892,123627,157008,196633,248221,311442,390859,488327,610685
%N A326498 Number of maximal subsets of {1..n} containing no sums of distinct elements.
%H A326498 Andrew Howroyd, <a href="/A326498/a326498.txt">PARI Program</a>
%e A326498 The a(1) = 1 through a(7) = 16 subsets:
%e A326498   {1}  {1,2}  {1,2}  {1,3}    {1,2,4}  {1,2,4}    {1,2,4}
%e A326498               {1,3}  {1,2,4}  {1,2,5}  {1,2,5}    {1,2,5}
%e A326498               {2,3}  {2,3,4}  {1,3,5}  {1,2,6}    {1,2,6}
%e A326498                               {2,3,4}  {1,3,5}    {1,2,7}
%e A326498                               {2,4,5}  {1,3,6}    {1,3,6}
%e A326498                               {3,4,5}  {1,4,6}    {1,4,6}
%e A326498                                        {2,3,4}    {1,4,7}
%e A326498                                        {2,3,6}    {2,3,4}
%e A326498                                        {2,4,5}    {2,4,5}
%e A326498                                        {2,5,6}    {2,4,7}
%e A326498                                        {3,4,5,6}  {2,5,6}
%e A326498                                                   {1,3,5,7}
%e A326498                                                   {2,3,6,7}
%e A326498                                                   {3,4,5,6}
%e A326498                                                   {3,5,6,7}
%e A326498                                                   {4,5,6,7}
%t A326498 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326498 Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Plus@@@Subsets[#,{2,n}]]=={}&]]],{n,0,10}]
%o A326498 (PARI) \\ See link for program file.
%o A326498 for(n=0, 25, print1(A326498(n), ", ")) \\ _Andrew Howroyd_, Aug 29 2019
%Y A326498 Subsets without sums of distinct elements are A151897.
%Y A326498 Maximal sum-free subsets are A121269.
%Y A326498 Subsets with sums are A326083.
%Y A326498 Maximal subsets without products of distinct elements are A325710.
%Y A326498 Maximal subsets without sums or products of distinct elements are A326025.
%Y A326498 Cf. A007865, A103580, A326117, A326495, A326497.
%K A326498 nonn
%O A326498 0,4
%A A326498 _Gus Wiseman_, Jul 09 2019
%E A326498 a(16)-a(40) from _Andrew Howroyd_, Aug 29 2019
%E A326498 a(41)-a(44) from _Jinyuan Wang_, Oct 11 2020