0,1

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.

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

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 A076908 A013782 this_sequence A079173 A073826 A159397

Adjacent sequences: A137838 A137839 A137840 this_sequence A137842 A137843 A137844

easy,nonn

Ross Drewe (rd(AT)labyrinth.net.au), Feb 13 2008