Generalized Compositions and Weighted Fibonacci Numbers

Details Generalized Compositions and Weighted Fibonacci Numbers Generalized Compositions and Weighted Fibonacci Numbers

2010-09-16

arxiv.org/abs/1009.3216v1

Mathematics

Combinatorics

Scientific paper

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.

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