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A262458 Number of possible conjunction tables in the n-valued logics. 2

%I #8 Sep 23 2015 10:50:53

%S 1,1,256,14348907,281474976710656,2910383045673370361328125,

%T 22452257707354557240087211123792674816,

%U 174251498233690814305510551794710260107945042018748343,1766847064778384329583297500742918515827483896875618958121606201292619776

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

%C 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).

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

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

%o (PARI) a(n)=(n-1)^(n^2-1) \\ _Charles R Greathouse IV_, Sep 23 2015

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

%K nonn,easy

%O 1,3

%A _Max Alekseyev_, Sep 23 2015

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Last modified April 25 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)