以Fibonacci和Lucas数为权的二项式恒等式  

Some binomial identities with Fibonacci and Lucasnumbers as weights

作　　者：郭东威 丁根宏[2] GUO Dongwei;DING Genhong(School of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466000,China;Collegeof Science,Hohai University,Nanjing 211100,China)

机构地区：[1]周口师范学院数学与统计学院,周口466000 [2]河海大学理学院,南京211100

出　　处：《黑龙江大学自然科学学报》2022年第5期541-547,共7页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Fundamental Research Funds for the Central Universities(JGLX19_030,2019B80014)。

摘　　要：得到了一些以Fibonacci数和Lucas数为权的二项式和。首先给出了最近由Robert在期刊Fibonacci Quarterly上提出的H-882问题的解,其次给出了有限二项式和n∑k=0(n+k n-k)Q_(k)的显示表达式及n∑k=0(n+k k)Q_(k)的另一种用中心二项式系数表达的有趣形式,这里Q_(k)代表Fibonacci数F_(k)或者Lucas数L_(k)。Some binomial sums with Fibonacci and Lucas numbers as weights are established.Among others,a solution to the problem H-882 proposed recently by Robert is first given.And then the explicit formula for the finite binomial sum n∑k=0(n+k n-k)Q_(k)is derived.In addition,another interesting expression concerning central binomial coefficient for the sum n∑k=0(n+k k)Q_(k)is obtained,where the Q_(k) stands for Fibonacci number F_(k) or Lucas number L_(k).

关 键 词：FIBONACCI数 LUCAS数 二项式系数 

分 类 号：O157.1[理学—数学]