A325865 Number of maximal subsets of {1..n} of which every subset has a different sum.

1, 1, 1, 3, 3, 6, 14, 23, 27, 40, 64, 104, 180, 275, 399, 554, 679, 872

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Example

The a(1) = 1 through a(6) = 14 subsets:
  {1}  {1,2}  {1,2}  {1,3}    {1,2,4}  {1,2,4}
              {1,3}  {1,2,4}  {1,2,5}  {1,2,5}
              {2,3}  {2,3,4}  {1,3,5}  {1,2,6}
                              {2,3,4}  {1,3,5}
                              {2,4,5}  {1,3,6}
                              {3,4,5}  {1,4,6}
                                       {2,3,4}
                                       {2,3,6}
                                       {2,4,5}
                                       {2,5,6}
                                       {3,4,5}
                                       {3,4,6}
                                       {3,5,6}
                                       {4,5,6}

Mathematica

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&)/@y];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Plus@@@Subsets[#]&]]], {n, 0, 10}]

Crossrefs

Cf. A002033, A108917, A143823, A196723, A275972.

Cf. A325860, A325864, A325866, A325867, A325877, A325878, A325879, A325880.

Sequence in context: A096572 A318540 A325879 * A110523 A145597 A143418

Adjacent sequences: A325862 A325863 A325864 * A325866 A325867 A325868

Keyword

nonn,more

Author

Gus Wiseman, Jun 01 2019

Status

approved