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

0,2

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

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}]

Crossrefs

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

Sequence in context: A068330 A017993 A049870 * A333098 A107428 A086379

Adjacent sequences: A093967 A093968 A093969 * A093971 A093972 A093973

Keyword

nonn

Author

T. D. Noe, Apr 20 2004

Extensions

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

Status

approved