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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)