The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A079195

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A079195

Number of non-associative commutative closed binary operations on a set of order n.
(history; published version)

#10 by Michael De Vlieger at Wed Jan 26 23:09:05 EST 2022

STATUS

proposed

approved

#9 by Andrew Howroyd at Wed Jan 26 23:00:34 EST 2022

STATUS

editing

proposed

#8 by Andrew Howroyd at Wed Jan 26 22:58:19 EST 2022

LINKS

C. van den Bosch, <a href="https://web.archive.org/web/20071014230143/http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

#7 by Andrew Howroyd at Wed Jan 26 21:46:32 EST 2022

DATA

0, 0, 2, 666, 1047436, 30517547395, 21936950639192784, 459986536544739894613595, 324518553658426726783148869733112

OFFSET

1,2

0,3

COMMENTS

A079192(n)+A079195(n)+A079198(n)+A023815(n)=A002489(n).

Each a(n) is equal to the sum of the products of each element in row n of A079197 and the corresponding element of A079210.

FORMULA

A079192(n) + a(n) + A079198(n) + A023815(n) = A002489(n).

a(n) = Sum_{k>=1} A079197(n,k)*A079210(n,k).

a(n) = A023813(n) - A023815(n). - Andrew Howroyd, Jan 26 2022

CROSSREFS

Cf. A023813, A023815, A079192, A079196, (isomorphism classes), A079197, A079198.

EXTENSIONS

a(0)=0 prepended and a(5)-a(8) added by Andrew Howroyd, Jan 26 2022

STATUS

approved

editing

#6 by Russ Cox at Sun Jul 10 18:42:31 EDT 2011

LINKS

<a href="/Sindx_index/Gre.html#groupoids">Index entries for sequences related to groupoids</a>

Discussion

Sun Jul 10

18:42

OEIS Server: https://oeis.org/edit/global/46

#5 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

<a href="/Sindx_Gre.html#groupoids">Index entries for sequences related to groupoids</a>

KEYWORD

nonn,new

nonn

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_Gre.html#groupoids">Index entries for sequences related to groupoids</a>

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

LINKS

C. van den Bosch, <a href="http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

C. van den Bosch, <a href="http://ocean.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

KEYWORD

nonn,new

nonn

AUTHOR

Christian van den Bosch (cjvdb1cjb(AT)student.cs.ucccjb.ie), Jan 03 2003

#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_Gre.html#groupoids">Index entries for sequences related to groupoids</a>

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Number of non-associative commutative closed binary operations on a set of order n.

DATA

0, 2, 666, 1047436

OFFSET

1,2

COMMENTS

A079192(n)+A079195(n)+A079198(n)+A023815(n)=A002489(n).

Each a(n) is equal to the sum of the products of each element in row n of A079197 and the corresponding element of A079210.

LINKS

C. van den Bosch, <a href="http://ocean.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

CROSSREFS

Cf. A023815, A079192, A079196, A079197, A079198.

KEYWORD

nonn

AUTHOR

Christian van den Bosch (cjvdb1(AT)student.cs.ucc.ie), Jan 03 2003

STATUS

approved