A326024 Number of subsets of {1..n} containing no sums or products of distinct elements.

1, 2, 3, 5, 9, 15, 25, 41, 68, 109, 179, 284, 443, 681, 1062, 1587, 2440, 3638, 5443, 8021, 11953, 17273, 25578, 37001, 53953, 77429, 113063, 160636, 232928, 330775, 475380, 672056, 967831, 1359743, 1952235, 2743363, 3918401, 5495993, 7856134, 10984547, 15669741

Offset: 0

Author

Gus Wiseman, Jul 09 2019

Keywords

• nonn

Examples

			The a(0) = 1 through a(5) = 15 subsets:
  {}  {}   {}   {}     {}       {}
      {1}  {1}  {1}    {1}      {1}
           {2}  {2}    {2}      {2}
                {3}    {3}      {3}
                {2,3}  {4}      {4}
                       {2,3}    {5}
                       {2,4}    {2,3}
                       {3,4}    {2,4}
                       {2,3,4}  {2,5}
                                {3,4}
                                {3,5}
                                {4,5}
                                {2,3,4}
                                {2,4,5}
                                {3,4,5}
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..80

Crossrefs

Subsets without sums of distinct elements are A151897.

Subsets without products of distinct elements are A326117.

Maximal subsets without sums or products of distinct elements are A326025.

Subsets with sums (and products) are A326083.

Sum-free and product-free subsets are A326495.

Cf. A007865, A051026, A121269, A325710, A326076, A326489, A326497, A326498.

Programs

Mathematica

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

PARI

a(n)={
   my(recurse(k, es, ep)=
    if(k > n, 1,
      my(t = self()(k + 1, es, ep));
      if(!bittest(es,k) && !bittest(ep,k),
         es = bitor(es, bitand((2<Andrew Howroyd, Aug 25 2019

Extensions

Terms a(16)-a(40) from Andrew Howroyd, Aug 25 2019