Representation of Natural Numbers Using Generalized Fibonacci Sequence
Abstract: Previously, there were many studies about the problem of representation of natural numbers. But it’s comparatively rare to study the problem based on Fibonacci sequence and its extension. This thesis mainly discussed the feasibility and diversity of this kind of representation. Utilizing enu-merating polynomials and binomial codes, we focused on minimal and maximal representations of natural numbers. In addition to Fibonacci sequence, we also studied the situation of Lucas sequence and offered some hypotheses in the case of n-step Fibonacci sequence.
文章引用: 郭婷婷 , 晁福刚 , 任韩 (2016) Fibonacci数列及其推广形式的正整数表示。 应用数学进展， 5， 225-231. doi: 10.12677/AAM.2016.52029
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