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Number of isomorphism classes of quandles of order n.
8

%I #40 Jun 15 2022 04:09:05

%S 1,1,1,3,7,22,73,298,1581,11079,102771,1275419,21101335,469250886

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

%C Quandles up to order 8 were determined first by Sam Nelson and co-authors (see references). Nelson's results were confirmed independently by the submitter, and extended to order 9.

%H M. Elhamdadi, <a href="http://arxiv.org/abs/1209.6518">Distributivity in Quandles and Quasigroups</a>, arXiv preprint arXiv:1209.6518 [math.RA], 2012. - From _N. J. A. Sloane_, Dec 29 2012

%H Richard Henderson, Todd Macedo and Sam Nelson, <a href="https://doi.org/10.1016/j.jsc.2006.03.002">Symbolic Computation with Finite Quandles</a>, J. Symb. Comp. 41 (2006), 811-817.

%H Benita Ho and Sam Nelson, <a href="http://projecteuclid.org/euclid.hha/1139839513">Matrices and Finite Quandles</a>, Homology, Homotopy and Applications, 7 (2005), No. 1, 197-208.

%H P. Jedlicka, A. Pilitowska, D. Stanovsky et al., <a href="http://arxiv.org/abs/1409.8396">The structure of medial quandles</a>, arXiv preprint 1409.8396 [math.GR], 2014-2015.

%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 Petr Vojtěchovský and Seung Yeop Yang, <a href="https://doi.org/10.1090/mcom/3409">Enumeration of racks and quandles up to isomorphism</a>, Math. Comp. 88 (2019), 2523-2540; arXiv:<a href="https://arxiv.org/abs/1911.04991">1911.04991</a> [math.QA], 2019.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Quandles">Quandles</a>

%Y Cf. A176077, A181771, A165200, A179010, A177886, A178432, A181770.

%K nonn,hard,more

%O 0,4

%A _James McCarron_

%E a(10)-a(13) from Petr Vojtěchovský and Seung Yeop Yang added by _Andrey Zabolotskiy_, Jun 15 2022