%I A093970
%S A093970 1,2,4,6,11,21,31,55,99,145,252,430,620,1042,1786,2597,4304,7241,10374,
%T A093970 17098,28967
%N A093970 Number of subsets A of {1,...,n} such that there are no solutions to 
               a+b+c=d for a,b,c,d in A.
%C A093970 In sumset notation, number of subsets A of {1,...,n} such that the intersection 
               of A and 3A is empty. Using the Mathematica program, all such subsets 
               can be printed.
%H A093970 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Sum-FreeSet.html">Sum-Free Set</a>
%t A093970 nn=20; SumFree3Q[s_List] := Module[{sumFree, i, j, k}, If[Length[s]<2, 
               True, If[3s[[1]]>s[[ -1]], True, sumFree=True; i=1; While[sumFree&&i<=Length[s], 
               j=i; While[sumFree&&j<=Length[s], k=j; While[sumFree&&k<=Length[s], 
               sumFree=!MemberQ[s, s[[i]]+s[[j]]+s[[k]]]; k++ ]; j++ ]; i++ ]; sumFree]]]; 
               ss={{}}; Table[If[n>0, ssNew={}; Do[t=Append[ss[[i]], n]; If[SumFree3Q[t], 
               AppendTo[ssNew, t]], {i, Length[ss]}]; ss=Join[ss, ssNew]]; Length[ss], 
               {n, 0, nn}]
%Y A093970 Cf. A007865 (number of sum-free subsets of 1..n).
%Y A093970 Sequence in context: A068330 A017993 A049870 this_sequence A107428 A086379 
               A096460
%Y A093970 Adjacent sequences: A093967 A093968 A093969 this_sequence A093971 A093972 
               A093973
%K A093970 nonn
%O A093970 0,2
%A A093970 T. D. Noe (noe(AT)sspectra.com), Apr 20 2004