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

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

Offset

0,6

Comments

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

Links

Table of n, a(n) for n=0..11.

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

Formula

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

Crossrefs

Cf. A057771, A000001.

Sequence in context: A355955 A113056 A336436 * A220549 A210904 A306990

Adjacent sequences: A318983 A318984 A318985 * A318987 A318988 A318989

Keyword

nonn,more

Author

Steve Szabo, Sep 06 2018

Extensions

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

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

Status

approved