A093970 - OEIS

%I #14 Oct 07 2020 08:02:42

%S 1,2,4,6,11,21,31,55,99,145,252,430,620,1042,1786,2597,4304,7241,

%T 10374,17098,28967,41444,68017,113746,162204,268412,449318,640341,

%U 1053604,1764648,2524852,4154138,6968215,9935216,16371249,27594872,39353636,64914388,109205201

%N 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 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.

%H Fausto A. C. Cariboni, <a href="/A093970/b093970.txt">Table of n, a(n) for n = 0..62</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Sum-FreeSet.html">Sum-Free Set</a>

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

%K nonn

%O 0,2

%A _T. D. Noe_, Apr 20 2004

%E a(21)-a(38) from _Fausto A. C. Cariboni_, Sep 30 2020