A057771 Number of loops (quasigroups with an identity element) of order n.

0, 1, 1, 1, 2, 6, 109, 23746, 106228849, 9365022303540, 20890436195945769617, 1478157455158044452849321016

Offset

0,5

Links

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

Connor M. Depies, Extensions of the Klein-4 group and signed products, Quasigroups Rel. Sys. 34 (2026), 67-91. See p. 73.

Alexander 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, Alison Meynert, and Wendy Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs 15(2) (2007), 98-119.

Index entries for sequences related to quasigroups

Crossrefs

Cf. A000315, A057991, A057992, A057993, A057994, A057996, A057997, A057998, A089925.

Sequence in context: A351780 A059088 A216151 * A056164 A156500 A264889

Adjacent sequences: A057768 A057769 A057770 * A057772 A057773 A057774

Keyword

nonn,more,nice

Author

Christian G. Bower, Nov 01 2000

Extensions

a(8) from Juergen Buntrock (jubu(AT)jubu.com), Nov 03 2003.

a(9)-a(10) (from the McKay-Meynert-Myrvold article) from Richard Bean, Feb 17 2004

a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009

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

Status

approved