On the enumeration of the functions with given endomorphism
An iterative procedure for enumeration of $n$-ary functions with endomorphism different from constant and permutation is proposed in $k$-valued logic. On the base of this endomorphism the formulas are fined for the numbers of $n$-ary functions in three-valued logic which have nontrivial endomorphisms. For arbitrary endomorphism semigroup the cardinality of set of all 3-ary functions having endomorphisms in given simigroup is defined in three-valued logic.