%I #19 Jan 27 2022 18:19:51
%S 0,0,2,2,3,2,4,2,4
%N Number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.
%C 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 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%F A079231(n) + A079233(n) + A079235(n) + A079237(n) + A079196(n) + A079241(n) + a(n) + A079245(n) + A063524(n) = A002489(n).
%F Conjecture: a(n) = A000005(n) for n > 1. - _Andrew Howroyd_, Jan 26 2022
%e From _Andrew Howroyd_, Jan 26 2022: (Start)
%e The a(6) = 4 operations are the two shown below and their converses.
%e | 1 2 3 4 5 6 | 1 2 3 4 5 6
%e --+------------ --+------------
%e 1 | 1 2 3 4 5 6 1 | 1 2 3 1 2 3
%e 2 | 1 2 3 4 5 6 2 | 1 2 3 1 2 3
%e 3 | 1 2 3 4 5 6 3 | 1 2 3 1 2 3
%e 4 | 1 2 3 4 5 6 4 | 4 5 6 4 5 6
%e 5 | 1 2 3 4 5 6 5 | 4 5 6 4 5 6
%e 6 | 1 2 3 4 5 6 6 | 4 5 6 4 5 6
%e (End)
%Y Row sums of A079208.
%Y Cf. A079242 (labeled case), A079231, A079233, A079235, A079237, A079196, A079241, A079245, A063524.
%K nonn,more
%O 0,3
%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
%E a(0)=0 prepended and a(5)-a(8) from _Andrew Howroyd_, Jan 26 2022