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, 165, 222, 344, 466, 702, 944, 1452, 1912, 2940, 3950, 5888, 7910, 12160, 15971, 24559, 33008, 49476, 66164, 101556, 134219, 205807, 275333, 413698, 555455, 849598, 1121920, 1715401, 2299986, 3458692, 4623565, 7052955, 9347017

Offset

0,2

Links

Bert Dobbelaere, Table of n, a(n) for n = 0..64

Example

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}

Mathematica

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

Crossrefs

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

Sequence in context: A040040 A168497 A256975 * A355980 A239882 A086642

Adjacent sequences: A364838 A364839 A364840 * A364842 A364843 A364844

Keyword

nonn

Author

Gus Wiseman, Aug 15 2023

Extensions

More terms from Bert Dobbelaere, Mar 21 2026

Status

approved