# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a079243
Showing 1-1 of 1

%I A079243 #19 Jan 27 2022 18:19:51
%S A079243 0,0,2,2,3,2,4,2,4
%N A079243 Number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.
%C A079243 The only closed binary operations that are both commutative and anti-commutative are those on sets of size <= 1. The significance of non-commutative (and non-anti-associative) in the name is that it excludes this possibility. Otherwise, the first two terms would be 1. - _Andrew Howroyd_, Jan 26 2022
%H A079243 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1NlI3NlbWlncm91cHM">Index entries for sequences related to semigroups</a>
%F A079243 A079231(n) + A079233(n) + A079235(n) + A079237(n) + A079196(n) + A079241(n) + a(n) + A079245(n) + A063524(n) = A002489(n).
%F A079243 Conjecture: a(n) = A000005(n) for n > 1. - _Andrew Howroyd_, Jan 26 2022
%e A079243 From _Andrew Howroyd_, Jan 26 2022: (Start)
%e A079243 The a(6) = 4 operations are the two shown below and their converses.
%e A079243     | 1 2 3 4 5 6         | 1 2 3 4 5 6
%e A079243   --+------------       --+------------
%e A079243   1 | 1 2 3 4 5 6       1 | 1 2 3 1 2 3
%e A079243   2 | 1 2 3 4 5 6       2 | 1 2 3 1 2 3
%e A079243   3 | 1 2 3 4 5 6       3 | 1 2 3 1 2 3
%e A079243   4 | 1 2 3 4 5 6       4 | 4 5 6 4 5 6
%e A079243   5 | 1 2 3 4 5 6       5 | 4 5 6 4 5 6
%e A079243   6 | 1 2 3 4 5 6       6 | 4 5 6 4 5 6
%e A079243 (End)
%Y A079243 Row sums of A079208.
%Y A079243 Cf. A079242 (labeled case), A079231, A079233, A079235, A079237, A079196, A079241, A079245, A063524.
%K A079243 nonn,more
%O A079243 0,3
%A A079243 Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
%E A079243 a(0)=0 prepended and a(5)-a(8) from _Andrew Howroyd_, Jan 26 2022

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE