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A111773 Number of n-element 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 n-element 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 Math-Fun Mailing List, May 01, 2005.

%F Empirically satisfies the relation a(P)=1 (mod P) for primes odd P.

%Y Cf. A111772 (non-isomorphic systems).

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 21 2005

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Last modified August 7 06:02 EDT 2020. Contains 336274 sequences. (Running on oeis4.)