A241690 Number of Sidon subsets of {1,...,n} of size 6.

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, 5688, 9036, 14106, 21190, 31158, 44370, 62206, 85308, 115662, 153746, 202146, 262156, 336960, 427488, 538690, 671604, 831926, 1021238, 1246604, 1510056, 1820580, 2179480

Offset

1,18

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..47.

Example

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

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], {6}], SidonQ[#] &], {n, 1, 30}]

Crossrefs

Cf. A054578.

Sequence in context: A221906 A116486 A179609 * A141317 A146534 A180888

Adjacent sequences: A241687 A241688 A241689 * A241691 A241692 A241693

Keyword

nonn

Author

Carl Najafi, Apr 27 2014

Status

approved