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%I #32 Nov 03 2014 17:09:09
%S 1,1,2,4,10,31,120,594,4013,35092,428080,6851545,153025576,4535778875,
%T 187380634539,10385121165057,801710433900516
%N Number of isomorphism classes of 2-reductive involutory abelian/medial quandles.
%C Both names "abelian" and "medial" refer to the identity (xy)(uv)=(xu)(yv). A quandle is called 2-reductive if all orbits are projection quandles. A (left) quandle is involutory (aka symmetric, kei) if all (left) translations have order at most 2, i.e., x(xy)=y is satisfied.
%H <a href="/A243931/b243931.txt">Table of n, a(n) for n = 1..17</a>
%H P. Jedlička, A. Pilitowska, D. Stanovský, A. Zamojska-Dzienio, <a href="http://arxiv.org/abs/1409.8396">The structure of medial quandles</a>, arXiv:1409.8396 [math.GR], 2014.
%H David Stanovský, <a href="http://www.karlin.mff.cuni.cz/~stanovsk/quandles/">Calculating with quandles</a> GAP code to calculate the numbers.
%Y Cf. A242044, A242275.
%K nonn,hard
%O 1,3
%A _David Stanovsky_, Oct 01 2014