A118127 Number of quasigroups of order <= n.

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

Offset

1,2

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).

Links

Table of n, a(n) for n=1..11.

Index entries for sequences related to quasigroups.

Formula

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

Example

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

Crossrefs

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

Sequence in context: A127005 A042553 A042139 * A100644 A013208 A094370

Adjacent sequences: A118124 A118125 A118126 * A118128 A118129 A118130

Keyword

nonn

Author

Jonathan Vos Post, May 12 2006

Status

approved