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A137841 Number of distinct n-ary operators in a quinternary logic. 1
5, 3125, 298023223876953125, 2350988701644575015937473074444491355637331113544175043017503412556834518909454345703125 (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

Table of n, a(n) for n=0..3.

FORMULA

a(n) = 5^(5^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. A137840 = the number of distinct n-ary operators in a quaternary logic.

Sequence in context: A060345 A171980 A013782 * A204940 A172954 A079173

Adjacent sequences:  A137838 A137839 A137840 * A137842 A137843 A137844

KEYWORD

easy,nonn

AUTHOR

Ross Drewe, Feb 13 2008

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.