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, 2, 10, 92, 1321, 27882, 819330

Offset

1,2

References

Richard C. Schroeppel, Posting to Math-Fun Mailing List, May 01, 2005.

Links

Table of n, a(n) for n=1..7.

Formula

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

Crossrefs

Cf. A111772 (non-isomorphic systems).

Sequence in context: A181136 A182952 A108209 * A289020 A195415 A336271

Adjacent sequences: A111770 A111771 A111772 * A111774 A111775 A111776

Keyword

nonn

Author

N. J. A. Sloane, Nov 21 2005

Status

approved