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.

1, 2, 4, 6, 11, 21, 31, 55, 99, 145, 252, 430, 620, 1042, 1786, 2597, 4304, 7241, 10374, 17098, 28967, 41444, 68017, 113746, 162204, 268412, 449318, 640341, 1053604, 1764648, 2524852, 4154138, 6968215, 9935216, 16371249, 27594872, 39353636, 64914388, 109205201

Offset: 0

Author

T. D. Noe, Apr 20 2004

Keywords

• nonn

Comments

In sumset notation, the sequence gives the 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.

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..62
• Eric Weisstein's World of Mathematics, Sum-Free Set

Crossrefs

Cf. A007865 (number of sum-free subsets of 1..n).

Programs

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}]

Extensions

a(21)-a(38) from Fausto A. C. Cariboni, Sep 30 2020