enreeksen

ENreeksen is a term used in mathematics and computer science to denote a structured family of numerical sequences generated by a common rule set. The name combines Dutch roots: "en" meaning "and" and "reeksen" meaning "sequences," and is used in some Dutch-language discussions of sequence families. The concept is not widely standardized, and definitions vary by author, but common features include a finite or infinite set of generating rules, a parameterization by a set E, and a unifying framework for comparing sequences produced by different rules.

Definition and examples: An ENreeksen is typically specified by a generation schema that takes as input a previous term or terms and a parameter e in E, producing the next term. For example, one ENreeksen class might define a_n = a_{n-1} + e_n with e_n chosen from a fixed set; another might use a_n = f(a_{n-1}, a_{n-2}, e_n). Examples are used to illustrate properties like growth rate, convergence, or periodicity.

Applications: The concept is used in teaching discrete math to compare generation rules, in the design of pseudo-random generators, and in the analysis of sequence spaces in combinatorics. Researchers discuss ENreeksen when describing families of sequences under a shared formalism.

Limitations: Because the term is not universally standardized, precise definitions are context-dependent, and care is needed when comparing results from different sources.

See also: sequences, recurrence relations, sequence spaces, combinatorics.