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%I #13 Dec 10 2023 22:04:46
%S 1,2,4,6,10,16,25,39,63,99,158,253,402,639,1021,1633,2617,4153,6633,
%T 10460,16598,26146,41409,64733,102006,159165,249698,387515,604769,
%U 933531,1451882,2232319,3451823
%N Number of difference sets of subsets of {1,2,...,n}, i.e., the size of {D(A) : A subset [n] }, where D(A)={a_i-a_j : a_i>a_j and a_i,a_j in A}.
%C 2^(floor(n/2)) <= a(n) <= 2^n.
%e a(4)=6 because {1}, {1,2}, {1,3}, {1,4}, {1,2,3} and {1,2,4} have difference sets {}, {1}, {2}, {3}, {1,2}, {1,2,3}, respectively and all 2^4 subsets of {1,2,3,4} have one of these difference sets.
%t SetToNumber = Compile[{{A, _Integer, 1}, {LP, _Integer}}, Plus @@ (2^Union[Flatten[Table[If[i > j, A[[i]] - A[[j]], 0], {j, LP}, {i, LP}]]])]; GetSetA = Compile[{{n, _Integer}}, Flatten[Position[IntegerDigits[n, 2], 1]]]; DS[n_] := Module[{LP, A}, A = GetSetA[n]; LP = Length[A]; SetToNumber[A, LP]]; newfset[d_] := Union[Table[DS[n], {n, 2^(d - 1) + 1, 2^d - 1, 2}]]; newf[d_] := newf[d] = Length[newfset[d]]; a[2] = 2; a[d_] := a[d] = newf[d] + a[d - 1];
%K nonn,more
%O 1,2
%A _Kevin O'Bryant_, Mar 10 2002
%E a(27)-a(33) from _Sean A. Irvine_, Dec 10 2023
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