A137841 Number of distinct n-ary operators in a quinternary logic.

5, 3125, 298023223876953125, 2350988701644575015937473074444491355637331113544175043017503412556834518909454345703125

Offset: 0

Author

Ross Drewe, Feb 13 2008

Keywords

• easy
• nonn

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.

Crossrefs

Cf. A001146 (in binary logic), A055777 (in ternary logic), A137840 (in quaternary logic).

Subsequence of A000351.

Formula

a(n) = 5^(5^n).