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A326495 Number of subsets of {1..n} containing no sums or products of pairs of elements. 8
1, 1, 2, 4, 6, 11, 17, 30, 45, 71, 101, 171, 258, 427, 606, 988, 1328, 2141, 3116, 4952, 6955, 11031, 15320, 23978, 33379, 48698, 66848, 104852, 144711, 220757, 304132, 461579, 636555, 973842, 1316512, 1958827, 2585432, 3882842, 5237092, 7884276, 10555738, 15729292 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The pairs are not required to be strict.

LINKS

Table of n, a(n) for n=0..41.

FORMULA

For n > 0, a(n) = A326490(n) - 1.

EXAMPLE

The a(1) = 1 through a(6) = 17 subsets:

  {}  {}   {}     {}     {}       {}

      {2}  {2}    {2}    {2}      {2}

           {3}    {3}    {3}      {3}

           {2,3}  {4}    {4}      {4}

                  {2,3}  {5}      {5}

                  {3,4}  {2,3}    {6}

                         {2,5}    {2,3}

                         {3,4}    {2,5}

                         {3,5}    {2,6}

                         {4,5}    {3,4}

                         {3,4,5}  {3,5}

                                  {4,5}

                                  {4,6}

                                  {5,6}

                                  {2,5,6}

                                  {3,4,5}

                                  {4,5,6}

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], Intersection[#, Union[Plus@@@Tuples[#, 2], Times@@@Tuples[#, 2]]]=={}&]], {n, 0, 10}]

CROSSREFS

Subsets without sums are A007865.

Subsets without products are A326489.

Subsets without differences or quotients are A326490.

Maximal subsets without sums or products are A326497.

Subsets with sums (and products) are A326083.

Cf. A051026, A103580, A326020, A326076, A326117, A326491.

Sequence in context: A004698 A014217 A034297 * A026636 A026658 A138688

Adjacent sequences:  A326492 A326493 A326494 * A326496 A326497 A326498

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 09 2019

EXTENSIONS

Terms a(19) and beyond from Andrew Howroyd, Aug 25 2019

STATUS

approved

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Last modified September 21 12:49 EDT 2020. Contains 337272 sequences. (Running on oeis4.)