A241689 Number of Sidon subsets of {1,...,n} of size 5.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 22, 68, 156, 320, 584, 1008, 1622, 2520, 3734, 5428, 7612, 10488, 14126, 18744, 24390, 31436, 39914, 50212, 62390, 76932, 93918, 113960, 137058, 163896, 194632, 229988, 270018, 315712, 367106, 425220, 490164, 563080, 644096

Offset

1,12

Comments

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.

Links

Table of n, a(n) for n=1..45.

Example

a(12)=4 since the only subsets of {1,...,12} satisfying the required conditions are {1,2,5,10,12}, {1,3,8,9,12}, {1,3,8,11,12}, and {1,4,5,10,12}.

Mathematica

SidonQ[l__] := If[Length[Join[Plus @@@ Subsets[l, {2}], 2 l]] == Length[Union[Join[Plus @@@ Subsets[l, {2}], 2 l]]], True, False]
Table[Length@Select[Subsets[Range[n], {5}], SidonQ[#] &], {n, 1, 30}]

Crossrefs

Cf. A054578.

Sequence in context: A174814 A106846 A086863 * A052149 A062966 A347722

Adjacent sequences: A241686 A241687 A241688 * A241690 A241691 A241692

Keyword

nonn

Author

Carl Najafi, Apr 27 2014

Status

approved