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Number of distinct n-ary operators in a quaternary logic.
4

%I #6 Jul 25 2023 12:20:49

%S 4,256,4294967296,340282366920938463463374607431768211456,

%T 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

%N Number of distinct n-ary operators in a quaternary logic.

%C The total number of n-ary operators in a k-valued logic is T = k^(k^n), i.e. if S is a set of k elements, there are T ways of mapping an ordered subset of n elements taken from S to an element of S. Some operators are "degenerate": the operator has arity p, if only p of the n input values influence the output. Therefore the set of operators can be partitioned into n+1 disjoint subsets representing arities from 0 to n.

%F a(n) = 4^(4^n).

%Y Cf. A001146 (in binary logic), A055777 (in a ternary logic), A137841 (in a quinternary logic).

%Y Subsequence of A000302.

%K easy,nonn

%O 0,1

%A _Ross Drewe_, Feb 13 2008