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 A137840 Number of distinct n-ary operators in a quaternary logic. 3
 4, 256, 4294967296, 340282366920938463463374607431768211456, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS FORMULA a(n) = 4^(4^n) CROSSREFS Cf. A001146 = the number of distinct n-ary operators in a binary logic. A055777 = the number of distinct n-ary operators in a ternary logic. A137841 = the number of distinct n-ary operators in a quinternary logic. Sequence in context: A136807 A057156 A132656 * A114561 A252586 A214136 Adjacent sequences:  A137837 A137838 A137839 * A137841 A137842 A137843 KEYWORD easy,nonn AUTHOR Ross Drewe, Feb 13 2008 STATUS approved

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