2010/09/16 by Milan Janjić, Janjic, Milan
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1009.3216
openalex publication_date 2010/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted r-generalized Fibonacci number. A relationship between these two numbers will be derived. We shall thus obtain a generalization of the well-known formula connecting Fibonacci numbers with the binomial coefficients.