[go: up one dir, main page]

login
A262458
Number of possible conjunction tables in the n-valued logics.
2
1, 1, 256, 14348907, 281474976710656, 2910383045673370361328125, 22452257707354557240087211123792674816, 174251498233690814305510551794710260107945042018748343, 1766847064778384329583297500742918515827483896875618958121606201292619776
OFFSET
1,3
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.
FORMULA
a(n) = (n-1)^(n^2-1).
PROG
(PARI) a(n)=(n-1)^(n^2-1) \\ Charles R Greathouse IV, Sep 23 2015
CROSSREFS
Cf. A076728 (number of negation tables), A262459 (number of logics).
Sequence in context: A227606 A016880 A227662 * A016940 A017012 A017096
KEYWORD
nonn,easy
AUTHOR
Max Alekseyev, Sep 23 2015
STATUS
approved