A118127 Number of quasigroups of order <= n.

1, 2, 3, 8, 43, 1454, 1131985, 12199587820, 2697830531268481, 15224736759268778589978, 2750892227033887206264514123491

Offset: 1

Author

Jonathan Vos Post, May 12 2006

Keywords

• nonn

Comments

A quasigroup is a groupoid G such that for all a and b in G, there exist unique c and d in G such that ac = b and da = b. Hence a quasigroup is not required to have an identity element, nor be associative. Equivalently, one can state that quasigroups are precisely groupoids whose multiplication tables are Latin squares (possibly empty).

Examples

			a(10) = 2750892227033887206264514123491 = 1 + 1 + 1 + 5 + 35 + 1411 + 1130531 + 12198455835 + 2697818331680661 + 15224734061438247321497 + 2750892211809150446995735533513.
		

Links

• Index entries for sequences related to quasigroups.

Crossrefs

Cf. A002860, A057991-A057994, A057771, A057996, A118641.

Formula

a(n) = SUM[i=0..n] A057991(i).