The asymptotic estimation for two classes of generalized Fibonacci sub-sequences

2025/10/15 by Wan, Yongkang, Liang, Zhonghao, Liao, Qunying
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.13472

Abstract

Since the Fibonacci sequence has good properties, it's important in theory and applications, such as in combinatorics, cryptography, and so on. In this paper, for the generalized Fibonacci sequence \W_n(a,b,p,q)\, by using elementary methods and techniques, we respectively give the asymptotic estimation values of (∑_k=n^∞\frac1W_mk+l^d)^-1 and (∑_k=n^∞\frac(-1)^kW_mk+l^d)^-1, which generalize the asymptotic estimation results of Yuan et al. \citeA14 in 2025.

Citations

• On the sum of reciprocal generalized Fibonacci numbers

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