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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
1, 2, 10, 92, 1321, 27882, 819330 (list; graph; refs; listen; history; text; internal format)
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 A181084

Adjacent sequences:  A111770 A111771 A111772 * A111774 A111775 A111776

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 21 2005

STATUS

approved

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Last modified February 20 12:57 EST 2019. Contains 320327 sequences. (Running on oeis4.)