

A067247


Number of difference sets of subsets of {1,2,...,n}, i.e., the size of {AA : A \subset [n] }, where AA={a_ia_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
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OFFSET

1,2


COMMENTS

2^(floor(n/2)) <= a(n) <= 2^n.


LINKS

Table of n, a(n) for n=1..26.


EXAMPLE

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.


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 A028488
Adjacent sequences: A067244 A067245 A067246 * A067248 A067249 A067250


KEYWORD

nonn,more


AUTHOR

Kevin O'Bryant, Mar 10 2002


STATUS

approved



