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A326173 Number of maximal subsets of {1..n} whose sum is less than or equal to the sum of their complement.

%I A326173 #9 Jun 22 2019 19:19:08
%S A326173 1,1,1,2,4,5,8,16,24,44,77,133,240,429,772,1414,2588,4742,8761,16273,
%T A326173 30255,56392,105581,198352,373228,703409,1329633,2519927,4781637,
%U A326173 9084813,17298255,33001380,63023204,120480659,230702421,442423139,849161669,1631219288,3137595779,6042247855,11644198080,22455871375,43351354727
%N A326173 Number of maximal subsets of {1..n} whose sum is less than or equal to the sum of their complement.
%C A326173 Also the number of minimal subsets of {1..n} whose sum is greater than or equal to the sum of their complement. For example, the a(0) = 1 through a(7) = 16 subsets are:
%C A326173   {}  {1}  {2}  {3}    {1,4}  {3,5}    {5,6}      {1,6,7}
%C A326173                 {1,2}  {2,3}  {4,5}    {1,4,6}    {2,5,7}
%C A326173                        {2,4}  {1,2,5}  {2,3,6}    {2,6,7}
%C A326173                        {3,4}  {1,3,4}  {2,4,5}    {3,4,7}
%C A326173                               {2,3,4}  {2,4,6}    {3,5,6}
%C A326173                                        {3,4,5}    {3,5,7}
%C A326173                                        {3,4,6}    {3,6,7}
%C A326173                                        {1,2,3,5}  {4,5,6}
%C A326173                                                   {4,5,7}
%C A326173                                                   {4,6,7}
%C A326173                                                   {5,6,7}
%C A326173                                                   {1,2,4,7}
%C A326173                                                   {1,2,5,6}
%C A326173                                                   {1,3,4,6}
%C A326173                                                   {2,3,4,5}
%C A326173                                                   {2,3,4,6}
%e A326173 The a(0) = 1 through a(7) = 16 subsets:
%e A326173   {}  {}  {1}  {3}    {1,2}  {1,5}    {4,6}      {1,5,7}
%e A326173                {1,2}  {1,3}  {2,5}    {1,2,5}    {1,6,7}
%e A326173                       {1,4}  {3,4}    {1,2,6}    {2,5,7}
%e A326173                       {2,3}  {1,2,3}  {1,3,5}    {3,4,7}
%e A326173                              {1,2,4}  {1,3,6}    {3,5,6}
%e A326173                                       {1,4,5}    {1,2,3,4}
%e A326173                                       {2,3,5}    {1,2,3,5}
%e A326173                                       {1,2,3,4}  {1,2,3,6}
%e A326173                                                  {1,2,3,7}
%e A326173                                                  {1,2,4,5}
%e A326173                                                  {1,2,4,6}
%e A326173                                                  {1,2,4,7}
%e A326173                                                  {1,2,5,6}
%e A326173                                                  {1,3,4,5}
%e A326173                                                  {1,3,4,6}
%e A326173                                                  {2,3,4,5}
%t A326173 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326173 Table[Length[fasmax[Select[Subsets[Range[n]],Plus@@Complement[Range[n],#]>=Plus@@#&]]],{n,0,10}]
%Y A326173 The non-maximal case is A059529.
%Y A326173 Cf. A053632, A057567, A057568, A063865, A326174, A326175.
%K A326173 nonn
%O A326173 0,4
%A A326173 _Gus Wiseman_, Jun 11 2019
%E A326173 a(16)-a(42) from _Bert Dobbelaere_, Jun 22 2019