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A093970
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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.
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1
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1, 2, 4, 6, 11, 21, 31, 55, 99, 145, 252, 430, 620, 1042, 1786, 2597, 4304, 7241, 10374, 17098, 28967
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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.
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LINKS
| Eric Weisstein's World of Mathematics, Sum-Free Set
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MATHEMATICA
| 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}]
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CROSSREFS
| Cf. A007865 (number of sum-free subsets of 1..n).
Sequence in context: A068330 A017993 A049870 * A107428 A086379 A096460
Adjacent sequences: A093967 A093968 A093969 * A093971 A093972 A093973
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Apr 20 2004
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