

A193067


The number of isomorphism classes of connected Alexander (aka indecomposable affine) quandles of order n


2



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, 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, 0, 57, 3, 59, 0, 40, 61, 33, 0, 65, 15, 21, 0, 69, 16, 71, 0, 34
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OFFSET

1,5


COMMENTS

Finite connected Alexander (affine) quandles are Latin. According to the ToyodaBruck 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


LINKS

W. Edwin Clark, Table of n, a(n) for n = 1..255
W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman, Quandle Colorings of Knots and Applications, arXiv preprint arXiv:1312.3307, 2013
S. Nelson, Classification of Finite Alexander Quandles
S. Nelson, Alexander Quandles of Order 16
K. Toyoda, On axioms of linear functions/a>, Proceedings of the Imperial Academy 17/7(1941), 221227.
Wikipedia, Medial


PROG

(GAP)
findY:=function(f, g)
local Y, y;
Y:=[];
for y in g do
Add(Y, Image(f, y^(1))*y);
od;
Y:=Set(Y);
return Subgroup(g, Y);
end;;
CA:=[];;
k:=8;;
for n in [1..2^k1] do
CA[n]:=0;
LGn:=AllSmallGroups(n, IsAbelian);
for g in LGn do
autg:=AutomorphismGroup(g);;
eautg:=List(ConjugacyClasses(autg), Representative);
for f in eautg do
N2:=findY(f, g);
if Size(N2) = n then CA[n]:=CA[n]+1; fi;
od;
od;
for j in [1..k] do
if n = 2^j and n <> 2^(j1) then Print("done to ", n, "\n"); fi;
od;
od;
for n in [1..2^k1] do
Print(CA[n], ", ");
od;


CROSSREFS

See Index to OEIS under quandles.
Sequence in context: A098496 A175297 A165754 * A177886 A011293 A181884
Adjacent sequences: A193064 A193065 A193066 * A193068 A193069 A193070


KEYWORD

nonn


AUTHOR

W. Edwin Clark, Jul 15 2011


STATUS

approved



