A089925 -id:A089925 - cp's OEIS frontend

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

Christian G. Bower, Nov 01 2000

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

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

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

A328746 Number of loops of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

Original entry on oeis.org

0, 1, 1, 1, 2, 5, 72, 12151, 53146457

Offset: 0

Jianing Song, Oct 26 2019

For the number of group-like algebraic structures of order n, see:
Semigroups: A027851 or A001423 (commutative: A001426);
Monoids: A058129 or A058133 (commutative: A058131);
Quasigroups: A057991 or A058171 (commutative: A057992);
Loops: A057771 or this sequence (commutative: A089925);
Groups: A000001 (commutative: A000688);
Rings: A027623 or A038036 (commutative: A037289);
Rings with unity: A037291;
Fields: A069513.

a(n) = (A057771(n)+A057996(n))/2.

A350018 Number of unipotent commutative loops of order 2n.

Original entry on oeis.org

1, 1, 1, 7, 3460, 6320290037, 15859695832489637513

Offset: 1

Ian Wanless, Dec 08 2021

Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.

Cf. A089925, A350017.

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

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A328746 Number of loops of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

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A350018 Number of unipotent commutative loops of order 2n.

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