A364841 Number of subsets S of {1..n} containing no element equal to the sum of a k-multiset of elements of S, for any 2 <= k <= |S|.

1, 2, 3, 6, 9, 15, 21, 34, 49, 75, 105

Offset: 0

Author

Gus Wiseman, Aug 15 2023

Keywords

• nonn
• more

Examples

			The a(0) = 1 through a(5) = 15 subsets:
  {}  {}   {}   {}     {}     {}
      {1}  {1}  {1}    {1}    {1}
           {2}  {2}    {2}    {2}
                {3}    {3}    {3}
                {1,3}  {4}    {4}
                {2,3}  {1,3}  {5}
                       {1,4}  {1,3}
                       {2,3}  {1,4}
                       {3,4}  {1,5}
                              {2,3}
                              {2,5}
                              {3,4}
                              {3,5}
                              {4,5}
                              {3,4,5}
		

Crossrefs

Cf. A007865, A085489, A103580, A151897, A236912, A326020, A326080, A326083, A364349, A364534.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]], Intersection[#,Join@@Table[Total/@Tuples[#,k], {k,2,Length[#]}]]=={}&]],{n,0,10}]