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%I #33 Dec 26 2021 23:33:54
%S 1,0,1,1,3,0,5,2,8,0,9,1,11,0,3,9,15,0,17,3,5,0,21,2,34,0,30,5,27,0,
%T 29,8,9,0,15,8,35,0,11,6,39,0,41,9,24,0,45,9,76,0,15,11,51,0,27,10,17,
%U 0,57,3,59,0,40,61,33,0,65,15,21,0,69,16,71,0,34
%N The number of isomorphism classes of connected Alexander (a.k.a. indecomposable affine) quandles of order n.
%C Finite connected Alexander (affine) quandles are Latin. According to the Toyoda-Bruck theorem, Latin affine quandles are the same objects as idempotent medial quasigroups. The values up to 16 were obtained by Nelson (see links below). - Edited by _David Stanovsky_, Oct 01 2014
%H W. Edwin Clark, <a href="/A193067/b193067.txt">Table of n, a(n) for n = 1..255</a>
%H W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman, <a href="http://arxiv.org/abs/1312.3307">Quandle Colorings of Knots and Applications</a>, arXiv preprint arXiv:1312.3307 [math.GT], 2013-2014.
%H S. Nelson, <a href="http://arxiv.org/abs/math/0202281">Classification of Finite Alexander Quandles</a>, arXiv:math/0202281 [math.GT], 2002-2003.
%H S. Nelson, <a href="http://arxiv.org/abs/math/0409460">Alexander Quandles of Order 16</a>, arXiv:math/0409460 [math.GT], 2004-2006.
%H K. Toyoda, <a href="http://dx.doi.org/10.3792/pia/1195578751">On axioms of linear functions</a>, Proceedings of the Imperial Academy 17/7(1941), 221-227.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Medial">Medial</a>
%o (GAP)
%o findY:=function(f,g)
%o local Y,y;
%o Y:=[];
%o for y in g do
%o Add(Y,Image(f,y^(-1))*y);
%o od;
%o Y:=Set(Y);
%o return Subgroup(g,Y);
%o end;;
%o CA:=[];;
%o k:=8;;
%o for n in [1..2^k-1] do
%o CA[n]:=0;
%o LGn:=AllSmallGroups(n,IsAbelian);
%o for g in LGn do
%o autg:=AutomorphismGroup(g);;
%o eautg:=List(ConjugacyClasses(autg),Representative);
%o for f in eautg do
%o N2:=findY(f,g);
%o if Size(N2) = n then CA[n]:=CA[n]+1; fi;
%o od;
%o od;
%o for j in [1..k] do
%o if n = 2^j and n <> 2^(j-1) then Print("done to ",n, "\n"); fi;
%o od;
%o od;
%o for n in [1..2^k-1] do
%o Print(CA[n], ",");
%o od;
%Y See Index to OEIS under quandles.
%K nonn
%O 1,5
%A _W. Edwin Clark_, Jul 15 2011
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