Extensions of An Approach to Generalized Fibonacci and Lucas Numbers with Binomial Coefficients

XUE Lin, ZHANG Zhi-zheng

doi:10.13371/j.cnki.chin.q.j.m.2020.01.005

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 1: 56 - 62

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.01.005

Extensions of An Approach to Generalized Fibonacci and Lucas Numbers with Binomial Coefficients

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Department of Mathematicsf Luoyang Normal University, Luoyang 471934, P. R. China

XUE Lin(1979-) female, native of Luoyang, Henan, an associate professor of Luoyang Normal University, M.S.D., engages in combinatorics; ZHANG Zhi~zheng(1964-), male, native of Xinxiang, Henan, who has been out of two postdoctoral stations, a professor of Luoyang Normal University, engages in combinatorics and special functions.

Received date: 2019-07-26

Online published: 2020-08-06

Supported by

Supported by the Youth Backbone Teacher Foundation of Henan^,s University(Grant No. 2016GGJS-117); Supported by the National Natural Science Foundation of China(Grant No. 11871258)

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Abstract

The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients. These results generalize the identities by Gulec, Taskaxa and Uslu in Appl. Math. Lett. 23(2010) 68-72 and Appl. Math. Comput. 220(2013) 482-486.

Key words： Second-order recurrence sequence; Generalized Fibonaci numbers; Generalized Lucas numbers; Binomial coefficient

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XUE Lin, ZHANG Zhi-zheng . Extensions of An Approach to Generalized Fibonacci and Lucas Numbers with Binomial Coefficients[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(1) : 56 -62 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.005

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