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A067247 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}. 0
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, 249698, 387515, 604769, 933531, 1451882, 2232319, 3451823 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
2^(floor(n/2)) <= a(n) <= 2^n.
LINKS
EXAMPLE
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.
MATHEMATICA
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];
CROSSREFS
Sequence in context: A305498 A028445 A006305 * A017985 A327474 A347207
KEYWORD
nonn,more
AUTHOR
Kevin O'Bryant, Mar 10 2002
EXTENSIONS
a(27)-a(33) from Sean A. Irvine, Dec 10 2023
STATUS
approved

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Last modified June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)