A325866 Number of subsets of {1..n} containing n such that every subset has a different sum.

1, 2, 3, 6, 9, 14, 20, 35, 44, 76, 96, 139, 179, 257, 312, 483, 561, 793, 970, 1459, 1535, 2307, 2619, 3503, 4130, 5478, 5973, 8165, 9081, 11666, 13176, 17738, 18440, 24778, 26873, 35187, 38070, 49978, 51776, 72457, 74207, 92512, 102210, 135571, 136786, 179604

Offset

1,2

Comments

These are strict knapsack partitions (A275972) organized by maximum rather than sum.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..150

Example

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

Mathematica

Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&UnsameQ@@Plus@@@Subsets[#]&]], {n, 10}]

Crossrefs

Cf. A108917, A143823, A143824, A196723, A275972.

Cf. A325860, A325864, A325865, A325867, A325877, A325878, A325880.

Sequence in context: A084628 A325269 A002096 * A094055 A094056 A194627

Adjacent sequences: A325863 A325864 A325865 * A325867 A325868 A325869

Keyword

nonn

Author

Gus Wiseman, Jun 01 2019

Extensions

a(18)-a(46) from Alois P. Heinz, Jun 03 2019

Status

approved