A111773


Number of nelement binary operation tables, out of a total n^n^2 tables, that satisfy the axioms for an Average system. Not culled for isomorphism. The Average system axioms are avg(A,A)=A, avg(A,B)=avg(B,A), avg(avg(A,B),avg(C,D)) = avg(avg(A,C),avg(B,D)).


1


%I
%S 1,2,10,92,1321,27882,819330
%N Number of nelement binary operation tables, out of a total n^n^2 tables, that satisfy the axioms for an Average system. Not culled for isomorphism. The Average system axioms are avg(A,A)=A, avg(A,B)=avg(B,A), avg(avg(A,B),avg(C,D)) = avg(avg(A,C),avg(B,D)).
%D Richard C. Schroeppel, Posting to MathFun Mailing List, May 01, 2005.
%F Empirically satisfies the relation a(P)=1 (mod P) for primes odd P.
%Y Cf. A111772 (nonisomorphic systems).
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 21 2005
