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%I A326024 #14 Apr 10 2021 15:07:42
%S A326024 1,2,3,5,9,15,25,41,68,109,179,284,443,681,1062,1587,2440,3638,5443,
%T A326024 8021,11953,17273,25578,37001,53953,77429,113063,160636,232928,330775,
%U A326024 475380,672056,967831,1359743,1952235,2743363,3918401,5495993,7856134,10984547,15669741
%N A326024 Number of subsets of {1..n} containing no sums or products of distinct elements.
%H A326024 Fausto A. C. Cariboni, <a href="/A326024/b326024.txt">Table of n, a(n) for n = 0..80</a>
%e A326024 The a(0) = 1 through a(5) = 15 subsets:
%e A326024   {}  {}   {}   {}     {}       {}
%e A326024       {1}  {1}  {1}    {1}      {1}
%e A326024            {2}  {2}    {2}      {2}
%e A326024                 {3}    {3}      {3}
%e A326024                 {2,3}  {4}      {4}
%e A326024                        {2,3}    {5}
%e A326024                        {2,4}    {2,3}
%e A326024                        {3,4}    {2,4}
%e A326024                        {2,3,4}  {2,5}
%e A326024                                 {3,4}
%e A326024                                 {3,5}
%e A326024                                 {4,5}
%e A326024                                 {2,3,4}
%e A326024                                 {2,4,5}
%e A326024                                 {3,4,5}
%t A326024 Table[Length[Select[Subsets[Range[n]],Intersection[#,Union[Plus@@@Subsets[#,{2,n}],Times@@@Subsets[#,{2,n}]]]=={}&]],{n,0,10}]
%o A326024 (PARI)
%o A326024 a(n)={
%o A326024    my(recurse(k, es, ep)=
%o A326024     if(k > n, 1,
%o A326024       my(t = self()(k + 1, es, ep));
%o A326024       if(!bittest(es,k) && !bittest(ep,k),
%o A326024          es = bitor(es, bitand((2<<n)-1, es << k));
%o A326024          forstep(i=n\k, 1, -1, if(bittest(ep,i), ep=bitor(ep,1<<(k*i))));
%o A326024          t += self()(k + 1, es, ep);
%o A326024       );
%o A326024       t);
%o A326024    );
%o A326024    1 + if(n, recurse(2, 1, 2));
%o A326024 } \\ _Andrew Howroyd_, Aug 25 2019
%Y A326024 Subsets without sums of distinct elements are A151897.
%Y A326024 Subsets without products of distinct elements are A326117.
%Y A326024 Maximal subsets without sums or products of distinct elements are A326025.
%Y A326024 Subsets with sums (and products) are A326083.
%Y A326024 Sum-free and product-free subsets are A326495.
%Y A326024 Cf. A007865, A051026, A121269, A325710, A326076, A326489, A326497, A326498.
%K A326024 nonn
%O A326024 0,2
%A A326024 _Gus Wiseman_, Jul 09 2019
%E A326024 Terms a(16)-a(40) from _Andrew Howroyd_, Aug 25 2019

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