login
Number of isomorphism classes of anti-associative closed binary operations on a set of order n, listed by class size.
3

%I #16 Aug 28 2024 16:37:11

%S 1,0,2,0,0,2,0,8,0,0,2,0,29,0,383,17366

%N Number of isomorphism classes of anti-associative closed binary operations on a set of order n, listed by class size.

%C Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

%H Christian 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>

%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>

%F T(n,k) = A079171(n,k) - A079178(n,k).

%F A079179(n) = Sum_{k>=1} A079210(n,k) * T(n,k).

%e First rows:

%e 1;

%e 0;

%e 2,0;

%e 0,2,0,8;

%e 0,0,2,0,29,0,383,17366;

%e ...

%Y Cf. A027423 (row lengths), A079176, A079177, A079180 (row sums).

%K nonn,tabf,more

%O 0,3

%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

%E a(0)=1 prepended and a(1) corrected by _Kamil Zabielski_, Aug 28 2024