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A325866 Number of subsets of {1..n} containing n such that every subset has a different sum. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..46.

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

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)