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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 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 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^k-1] 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^(j-1) then Print("done to ", n, "\n"); fi;    od; od; for n in [1..2^k-1] 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

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)