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Search: id:A067247
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| A067247 |
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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}. |
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+0
1
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| 1, 2, 4, 6, 10, 16, 25, 39, 63, 99, 158, 253, 402, 639, 1021, 1633, 2617, 4153, 6633, 10460, 16598, 26146, 41409, 64733, 102006, 159165
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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2^(Floor[n/2]) <= a(n) <= 2^n
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EXAMPLE
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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.
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MATHEMATICA
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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];
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CROSSREFS
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Sequence in context: A132002 A028445 A006305 this_sequence A017985 A028488 A080432
Adjacent sequences: A067244 A067245 A067246 this_sequence A067248 A067249 A067250
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KEYWORD
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nonn
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AUTHOR
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Kevin O'Bryant (obryant(AT)math.uiuc.edu), Mar 10 2002
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