A242044 Number of isomorphism classes of involutory abelian/medial quandles of order n.

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

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. Zamojska-Dzienio, 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