A362823 Number of labeled magmas with n elements satisfying the identities (xy)y = x and (xy)z = (xz)y.

1, 1, 4, 22, 976, 19376, 7680016, 430723168, 1489656111616, 214815786486400, 6364561150037368576, 2241692646969785651456, 566719960584895502028138496, 471612192582034433034750951424, 1008512943343839231897776246546624512, 1936475539456937172034340659334701398016

Offset: 0

Author

Andrew Howroyd, May 06 2023

Keywords

• nonn

Comments

a(n) is the number of ordered n-tuples of involutions on [n] that pairwise commute. Two involutions x,y on [n] commute if x*y = y*x.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Main diagonal of A362824.

Cf. A362383, A362643, A362821, A362822 (isomorphism classes).