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A241688 Number of Sidon subsets of {1,...,n} of size 4. 1
0, 0, 0, 0, 0, 0, 2, 10, 26, 60, 110, 190, 304, 466, 676, 958, 1312, 1762, 2310, 2984, 3786, 4750, 5874, 7196, 8720, 10484, 12488, 14780, 17360, 20276, 23530, 27174, 31210, 35696, 40630, 46074, 52032, 58566, 65676, 73434, 81840, 90966, 100814, 111460, 122906 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
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
Index entries for linear recurrences with constant coefficients, signature (2, 0, -1, 0, -2, 2, 0, 1, 0, -2, 1).
FORMULA
It appears to be the case that G.f.: 2*x^7*(1+3*x+3*x^2+5*x^3)/((1-x)^5*(1+x)^2*(1+x^2)*(1+x+x^2)), corrected by Vaclav Kotesovec, May 03 2014
a(n) ~ 1/24*n^4 (deduced from g.f.). - Ralf Stephan, Apr 29 2014
a(n) = a(n-11)+a(n-8)-a(n-3)+2*(a(n-6)+a(n-1)-a(n-10)-a(n-5)). - Fung Lam, May 02 2014
Explicit formula (derived from g.f.): a(n) = n^4/24 - 7*n^3/12 + 29*n^2/12 - 15*n/8 - floor(n/4) - 4/3*floor(n/3) + (n/2-9/4)*floor(n/2) - floor((n+1)/4) - 2/3*floor((n+1)/3). - Vaclav Kotesovec, May 03 2014
EXAMPLE
a(7)=2 since the only subsets of {1,...,7} satisfying the required conditions are {1,2,5,7} and {1,3,6,7}.
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], {4}], SidonQ[#] &], {n, 1, 30}]
CROSSREFS
Cf. A054578.
Sequence in context: A009307 A131130 A099969 * A183331 A324914 A025589
KEYWORD
nonn
AUTHOR
Carl Najafi, Apr 27 2014
STATUS
approved

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Last modified July 21 04:55 EDT 2024. Contains 374463 sequences. (Running on oeis4.)