

A193024


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


2



1, 1, 2, 3, 4, 2, 6, 7, 11, 4, 10, 6, 12, 6, 8, 23, 16, 11, 18, 12, 12, 10, 22, 14, 39, 12, 45, 18, 28, 8, 30, 48, 20, 16, 24, 33, 36, 18, 24, 28, 40, 12, 42, 30, 44, 22, 46, 46, 83, 39, 32, 36, 52, 45, 40, 42, 36, 28, 58, 24, 60, 30, 66, 167, 48, 20, 66, 48
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OFFSET

1,3


COMMENTS

Nelson enumerated Alexander quandles to order 16 (see the links below). The values of a(n) for n from 1 to 255 were obtained via a GAP program using ideas from Hou (see the link below).


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
M. Elhamdadi, Distributivity in Quandles and Quasigroups, arXiv preprint arXiv:1209.6518, 2012.  From N. J. A. Sloane, Dec 29 2012
Xiangdong Hou, Finite Modules over Z[t,t^{1}]
S. Nelson, Classification of Finite Alexander Quandles
S. Nelson, Alexander Quandles of Order 16s
Wikipedia, Racks and Quandles


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;;
Alex:=[];; k:=8;; for nn in [1..2^k1] do Alex[nn]:=0; od; for n in [1..2^k1] do 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); MM:= ((Size(g)^2)/Size(N2)); for nn in [1..2^k1] do if nn mod MM = 0 then Alex[nn]:=Alex[nn]+1; fi; od; od; od; od; for nn in [1..2^k1] doPrint(Alex[nn], ", "); od;;


CROSSREFS

See Index to OEIS under quandles.
Sequence in context: A178970 A172054 A047994 * A153038 A324911 A220335
Adjacent sequences: A193021 A193022 A193023 * A193025 A193026 A193027


KEYWORD

nonn


AUTHOR

W. Edwin Clark, Jul 15 2011


STATUS

approved



