cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

Christian G. Bower, Nov 01 2000

Keywords

Links

Crossrefs

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

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

A057991 Number of quasigroups of order n.

Original entry on oeis.org

1, 1, 1, 5, 35, 1411, 1130531, 12198455835, 2697818331680661, 15224734061438247321497, 2750892211809150446995735533513, 19464657391668924966791023043937578299025
Offset: 0

Views

Author

Christian G. Bower, Nov 01 2000

Keywords

Links

Crossrefs

Cf. A002860, A057992, A057993, A057994, A057771, A057996.

Extensions

More terms (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

A057996 Number of self-converse loops (quasigroups with an identity element) of order n.

Original entry on oeis.org

0, 1, 1, 1, 2, 4, 35, 556, 64065
Offset: 0

Views

Author

Christian G. Bower, Nov 01 2000

Keywords

Comments

x*y is isomorphic to y*x.

Links

Crossrefs

Cf. A057991, A057992, A057993, A057994, A057771, A057998.

Extensions

a(8) from Juergen Buntrock (jubu(AT)eule.in-berlin.de), Nov 17 2003
Offset corrected and a(0) prepended by Jianing Song, Oct 26 2019

A089925 Number of commutative loops (quasigroups with an identity element) of order n.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 8, 17, 2265, 30583, 358335026, 69522550106, 55355570223093935, 206176045800229002160
Offset: 0

Views

Author

Christian G. Bower and Juergen Buntrock (jubu(AT)jubu.com), Nov 14 2003

Keywords

Links

Crossrefs

Cf. A057771, A035481, A350009, A350010, A057992.

Extensions

a(9) from Michael Thwaites (michael.thwaites(AT)ucop.edu), Jan 23 2004
a(0) prepended by Jianing Song, Oct 26 2019
a(10)-a(13) from Ian Wanless, Dec 08 2021

A058177 Triangle: Number of commutative quasigroups of order n with k idempotents.

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 5, 1, 0, 0, 3, 5, 1, 1, 0, 1, 148, 213, 96, 34, 0, 0, 0
Offset: 0

Views

Author

Christian G. Bower, Nov 20 2000

Keywords

Examples

			1; 0,1; 0,1,0; 1,1,0,1; 1,5,1,0,0; ...

Links

Crossrefs

Row sums give A057992.

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

Views

Author

Jianing Song, Oct 26 2019

Keywords

Crossrefs

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.

Formula

a(n) = (A057771(n)+A057996(n))/2.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.