A262458 Number of possible conjunction tables in the n-valued logics.

1, 1, 256, 14348907, 281474976710656, 2910383045673370361328125, 22452257707354557240087211123792674816, 174251498233690814305510551794710260107945042018748343, 1766847064778384329583297500742918515827483896875618958121606201292619776

Offset: 1

Author

Max Alekseyev, Sep 23 2015

Keywords

• nonn
• easy

Comments

In a conjunction table, the only requirements are (i) True ^ True = True; and (ii) no other conjunction gives True. So each of the other n^2-1 entries can be assigned any of n-1 non-True values, giving raise to the formula (n-1)^(n^2-1).

References

• H. Eves, C. V. Newsom, An Introduction to the Foundation and Fundamental concepts of Mathematics, Rinehart & Co., New York, 1958.

Crossrefs

Cf. A076728 (number of negation tables), A262459 (number of logics).

Programs

PARI

a(n)=(n-1)^(n^2-1) \\ Charles R Greathouse IV, Sep 23 2015

Formula

a(n) = (n-1)^(n^2-1).