A137840 Number of distinct n-ary operators in a quaternary logic.

4, 256, 4294967296, 340282366920938463463374607431768211456, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

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 a ternary logic), A137841 (in a quinternary logic).

Subsequence of A000302.

Formula

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