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Number of Sidon subsets of {1,...,n} of size 6.
1

%I #8 Apr 29 2014 02:42:00

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,24,80,206,504,1004,1910,3380,

%T 5688,9036,14106,21190,31158,44370,62206,85308,115662,153746,202146,

%U 262156,336960,427488,538690,671604,831926,1021238,1246604,1510056,1820580,2179480

%N Number of Sidon subsets of {1,...,n} of size 6.

%C A Sidon set is a set of natural numbers A={a_1,a_2,...}, finite or infinite, such that all pairwise sums a_i+a_j (i <= j) are different.

%e a(18)=8 since there are 8 subsets of {1,...,18} satisfying the required conditions, for example {1,2,5,11,13,18}.

%t SidonQ[l__] := If[Length[Join[Plus @@@ Subsets[l, {2}], 2 l]] == Length[Union[Join[Plus @@@ Subsets[l, {2}], 2 l]]], True, False]

%t Table[Length@Select[Subsets[Range[n], {6}], SidonQ[#] &], {n, 1, 30}]

%Y Cf. A054578.

%K nonn

%O 1,18

%A _Carl Najafi_, Apr 27 2014