广义Jacobsthal数及其组合意义

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (6): 151-155.

广义Jacobsthal数及其组合意义

杨胜良^*,任凤云

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2020-11-13 出版日期:2021-12-28 发布日期:2021-12-28
通讯作者: 杨胜良(1963-),男,甘肃静宁人,教授.Email:slyang@lut.edu.cn
基金资助:
国家自然科学基金(11861045)

Generalized Jacobsthal number and its combinatorial meaning

YANG Sheng-liang, REN Feng-yun

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2020-11-13 Online:2021-12-28 Published:2021-12-28

摘要/Abstract

摘要： 引入了广义k阶Jacobsthal序列的概念,得到了k-Jacobsthal序列的发生函数以及相关的组合恒等式.通过研究两种格路的计数,给出了k-Jacobsthal数的两种组合解释.

关键词: Jacobsthal数, k阶Jacobsthal序列, Riordan矩阵, 发生函数, 格路, A-矩阵

Abstract: The concept of generalized Jacobsthal sequence of order k is introduced. The generating function of Jacobsthal sequence of order k and the related combinatorial identities are obtained. The enumerations of two classes of lattice paths are studied and the two combinatorial interpretations of Jacobsthal numbers of order k are given.

Key words: Jacobsthal number, Jacobsthal sequence of order k, Riordan array, generating function, lattice path A-matrix

中图分类号:

O157.1

杨胜良,任凤云. 广义Jacobsthal数及其组合意义[J]. 兰州理工大学学报, 2021, 47(6): 151-155.

YANG Sheng-liang, REN Feng-yun. Generalized Jacobsthal number and its combinatorial meaning[J]. Journal of Lanzhou University of Technology, 2021, 47(6): 151-155.

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