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The number of faithful connected quandles of order n.
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%I #14 Jan 31 2014 10:00:30

%S 1,0,1,1,3,2,5,2,8,1,9,8,11,0,7,9,15,12,17,9,9,0,21,27,34,0,62,13,27,

%T 20,29,8,11,0,15

%N The number of faithful connected quandles of order n.

%C Let Q be a quandle with product *. Let R_a: x ->x*a for a,x in Q. By definition R_a is an automorphism of the quandle Q. If the mapping a->R_a is an injection then the quandle is said to be faithful. A quandle is faithful precisely when the columns of the Cayley table of the quandle are distinct.

%C This sequence was computed using Leandro Vendramin's list of all connected quandles of order at most 35.

%C Warning: Vendramin's quandles are assumed to be left distributive and hence one must reverse the order of the product to get the (right distributive) quandles used by knot theorists.

%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, 2013

%H F. J. B. J. Clauwens, <a href="http://arxiv.org/abs/1011.2456">Small Connected Quandles</a>, arxiv 1011.2456, Nov 10 2010

%H Leandro Vendramin, <a href="http://arxiv.org/abs/1105.5341">On the classification of quandles of low order</a>, arXiv:1105.5341v1 [math.GT], May 26 2011

%Y Cf. A181771 (gives the number of connected quandles of order n).

%Y See also Index to OEIS under quandles.

%K nonn,more,hard

%O 1,5

%A _W. Edwin Clark_, May 29 2013