Search: id:A067247
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%I A067247
%S A067247 1,2,4,6,10,16,25,39,63,99,158,253,402,639,1021,1633,2617,4153,6633,
%T A067247 10460,16598,26146,41409,64733,102006,159165
%N A067247 Number of difference sets of subsets of {1,2,...,n}, i.e. the size of 
               {A-A : A \subset [n] }, where A-A={a_i-a_j : a_i>a_j and a_i,a_j 
               \in A}.
%C A067247 2^(Floor[n/2]) <= a(n) <= 2^n
%e A067247 a(4)=6 because {1}, {1,2}, {1,3}, {1,4}, {1,2,3} and {1,2,4} have difference 
               sets \emptyset, {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 A067247 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];
%Y A067247 Sequence in context: A132002 A028445 A006305 this_sequence A017985 A028488 
               A080432
%Y A067247 Adjacent sequences: A067244 A067245 A067246 this_sequence A067248 A067249 
               A067250
%K A067247 nonn
%O A067247 1,2
%A A067247 Kevin O'Bryant (obryant(AT)math.uiuc.edu), Mar 10 2002

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