login
Number of isomorphism classes of commutative closed binary operations (groupoids) on a set of order n, listed by class size.
3

%I #7 Jul 10 2011 18:42:30

%S 1,0,4,1,4,8,116,0,0,0,8,0,28,504,43428

%N Number of isomorphism classes of commutative closed binary operations (groupoids) on a set of order n, listed by class size.

%C A079184(n)+A079185(n)=A079171(n).

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

%C First four rows: 1; 0,4; 1,4,8,116; 0,0,0,8,0,28,504,43428

%C A079176(x) is equal to the sum of the products of each element in row x of this sequence and the corresponding element of A079210.

%C The sum of each row n is given by A079177(n).

%H C. van den Bosch, <a href="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>

%Y Cf. A001425, A023183, A079184. a(n, A027423(n)) = A030255(n).

%K nonn,tabf

%O 1,3

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