Compositions of integers and Fibonacci numbers

Abstract

In this paper, we deal with the compositions of the integers. We present the decompositions for both the composition sets and the odd composition sets of the integers. Thus the decompositions provide us to have not only an alternative proof of some well known identies but also many new identities for Fibonacci numbers and Lucas numbers. Thus we investigate the generating functions for the product sum of the odd composition sets of the integers and attain some functional equations.

Keywords

• Compositions of integers
• the odd combination set
• Fibonacci numbers
• Lucas numbers
• generating function

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