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Number of isomorphism classes of connected quandles of order n.
10

%I #49 Jun 22 2017 14:46:36

%S 1,0,1,1,3,2,5,3,8,1,9,10,11,0,7,9,15,12,17,10,9,0,21,42,34,0,65,13,

%T 27,24,29,17,11,0,15,73,35,0,13,33,39,26,41,9,45,0,45

%N Number of isomorphism classes of connected quandles of order n.

%C It is not clear whether the empty quandle is connected, so the sequence starts at order 1 instead of 0.

%D Hulpke, A. Personal communication, 2014.

%D Holt, D.; Royle, G. Personal communication, 2014.

%H John J. Cannon and Derek F. Holt, <a href="http://projecteuclid.org/euclid.em/1227121384">The transitive permutation groups of degree 32</a>, Experiment. Math. 17 (2008), no. 3, 307--314.

%H A. Hulpke, <a href="http://dx.doi.org/10.1016/j.jsc.2004.08.002">Constructing transitive permutation groups</a>, J. Symbolic Comput. 39 (2005), 1-30.

%H J. McCarron, <a href="http://arxiv.org/abs/1210.2150">Connected Quandles with Order Equal to Twice an Odd Prime</a>, arXiv preprint arXiv:1210.2150 [math.GR], 2012. - From _N. J. A. Sloane_, Dec 31 2012

%H Sam Nelson, <a href="http://www1.cmc.edu/pages/faculty/VNelson/quandles.html">Quandles and Racks</a>.

%H Leandro Vendramin, <a href="http://arxiv.org/abs/1105.5341">On the classification of quandles of low order</a>, arXiv:1105.5341 [math.GT], 2011-2012.

%H Leandro Vendramin and Matías Graña, <a href="http://code.google.com/p/rig/">Rig, a GAP package for racks and quandles</a>.

%o (GAP) (using the Rig package)

%o LoadPackage("rig");

%o for n in [1..47] do Display(NrSmallQuandles(n)); od;

%o # _Leandro Vendramin_, Sep 14 2014

%Y Cf. A181769, A176077.

%K nonn,hard,more

%O 1,5

%A _James McCarron_

%E Ninth term corrected by _James McCarron_, Dec 05 2010

%E More terms from _Leandro Vendramin_, Sep 14 2014