A350874 a(n) is the number of nonisomorphic magmas with n elements which satisfy the identity (xx)y = x(xy) for all x and y (so-called left-alternative magmas).

1, 1, 5, 97, 25311, 165974649

Offset

0,3

Comments

Equivalently (by symmetry), a(n) also equals the number of nonisomorphic right-alternative magmas with n elements (that is, magmas satisfying the identity x(yy) = (xy)y for all x and y).

Links

Table of n, a(n) for n=0..5.

Example

There are 10 non-isomorphic magmas with 2 elements, and 5 of these are left-alternative, so a(2) = 5.

Crossrefs

Cf. A001329 (magmas), A350875 (left-right-alternative magmas), A350876, A350873.

Sequence in context: A295190 A202516 A062538 * A053980 A215299 A088995

Adjacent sequences: A350871 A350872 A350873 * A350875 A350876 A350877

Keyword

nonn,more,hard

Author

Joel Brennan, Jan 20 2022

Extensions

a(5) from Andrew Howroyd, Jan 29 2022

Status

approved