A318986 Number of loops of order n that are not groups.

0, 0, 0, 0, 0, 5, 107, 23745, 106228844, 9365022303538, 20890436195945769615, 1478157455158044452849321015

Offset: 0

Author

Steve Szabo, Sep 06 2018

Keywords

• nonn
• more

Comments

A loop is a quasigroup with an identity element. - Muniru A Asiru, Dec 13 2018

Links

• A. Hulpke, Petteri Kaski and Patric R. J. Östergård, The number of Latin squares of order 11, Math. Comp. 80 (2011) 1197-1219.
• Brendan D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs 15 (2007), no. 2, 98-119.
• Wikipedia, Quasigroup
• Index entries for sequences related to quasigroups

Crossrefs

Cf. A057771, A000001.

Formula

a(n) = A057771(n) - A000001(n).

Extensions

a(7)-a(11) from Muniru A Asiru, Dec 07 2018

a(0) prepended by Jianing Song, Oct 26 2019