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关于Fibonacci数列的基及其均值的计算(英文)

On the Fibonacci base and compution of counting function mean value
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摘要 介绍了一个与Fibonacci数有关的计数函数,利用了猜想和归纳的方法,得出了一类精确的均值计算公式Ar(N)=∑n<Nar(n)(r=1,2,3),并利用数学归纳法给予证明。 A new counting function a(m) related to the Fibonacci number was introduced, then using the induction methods to give an exact calculating formula for the mean value of Ar(N)=∑n<Nar(n),(r=1,2,3) and prove them.
作者 杨倩丽
出处 《宝鸡文理学院学报(自然科学版)》 CAS 2005年第4期247-250,共4页 Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金 TheEducationDepartmentofShaanxi(05JK189)andWeinanTeachersCollege(04YKS014)
关键词 FIBONACCI数列 均值 计数函数 Fibonacci sequence mean value counting function
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参考文献4

  • 1DUNCAN R L .Application of uniform distribution to the Fibonacci numbers[J].The Fibonacci Quarterly,1967,5:137-140.
  • 2KUIPERS L.Remark on a paper by R.L. Duncan concerning the uniform distribution mod 1 of the sequence of the logarithms of the Fibonacci numbers[J].The Fibonacci Quarterly,1969,7:465-466.
  • 3LONDON H , FINKELSTEIN R .On Fibonacci and Lucas numbers, which are perfect powers[J].The Fibonacci Quarterly,1969,7:476-481.
  • 4ZHANG Wen-peng. Some identities involving the Fibonacci numbers[J].The Fibonacci Quarterly,1997,35:225-229.

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