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Search: id:A137840
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| A137840 |
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Number of distinct n-ary operators in a quaternary logic. |
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2
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| 4, 256, 4294967296, 340282366920938463463374607431768211456, 13407807929942597099574024998205846127479365820592393377723561443721764030073546\ 976801874298166903427690031858186486050853753882811946569946433649006084096
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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.
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FORMULA
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a(n) = 4^(4^n)
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CROSSREFS
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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 this_sequence A114561 A068417 A116967
Adjacent sequences: A137837 A137838 A137839 this_sequence A137841 A137842 A137843
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KEYWORD
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easy,nonn
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AUTHOR
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Ross Drewe (rd(AT)labyrinth.net.au), Feb 13 2008
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