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.
%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="/index/Se#semigroups">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