A new family of functions and their relationship to compositions and k-Fibonacci numbers

摘要

A composition of N is an ordered collection of one or more positive integers whose sum is N. The number of summands is called the number of parts of the composition. Several recent papers have investigated the number of compositions with various restrictions on the summands. For example, Grimaldi [8] explores the question of how many compositions of n exist when no l's are allowed in the composition. In [4,5], the authors explore the question of how many compositions of n exist when a particular summand is not allowed, or when only two summands are allowed in the composition. Other related questions are included in [1,2,3,6,7,9]