

A242044


Number of isomorphism classes of involutory abelian/medial quandles of order n.


1



1, 1, 3, 4, 11, 33, 121, 597, 4017, 35103, 428081, 6851591, 153025577, 4535779061, 187380634552
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OFFSET

1,3


COMMENTS

Both names "abelian" and "medial" refer to the identity (xy)(uv)=(xu)(yv). A (left) quandle is involutory (aka symmetric, kei) if all (left) translations have order at most 2, i.e., x(xy)=y is satisfied.
Enumerates intersection of the classes enumerated in A165200, A178432.


LINKS

Table of n, a(n) for n=1..15.
P. Jedlička, A. Pilitowska, D. Stanovský, A. ZamojskaDzienio, The structure of medial quandles, arXiv:1409.8396 [math.GR], 2014.
David Stanovský, Calculating with quandles GAP code to calculate the numbers.


CROSSREFS

Cf. A165200, A178432.
Sequence in context: A049979 A084378 A038559 * A344263 A275309 A119042
Adjacent sequences: A242041 A242042 A242043 * A242045 A242046 A242047


KEYWORD

nonn,hard


AUTHOR

David Stanovsky, Oct 01 2014


STATUS

approved



