广义斐波那契数列在网格中的新性质&nbsp;

杨子贤, 白建超

doi:10.13371/j.cnki.chin.q.j.m.2025.01.010

数学季刊 >

2025 , Vol. 40 >Issue 1: 103 - 110

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.01.010

广义斐波那契数列在网格中的新性质

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School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China

YANG Zi-xian (2002-), male, native of Mianyang, Sichuan, undergraduate of Northwestern Polytechnical University, engages in algebra; BAI Jian-chao (1987-), male, native of Shangluo, Shaanxi, associate professor of Northwestern Polytechnical University, engages in numerical algebra and optimization.

收稿日期: 2024-05-04

网络出版日期: 2025-03-30

基金资助

Supported by the National Natural Science Foundation of China (Grant No. 12471298), the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 23JSQ031), and the Shaanxi Province College Student Innovation and Entrepreneurship Training Program (Grant Nos. S202210699481 and S202310699324X).

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A Novel Property of Generalized Fibonacci Sequence in Grids

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School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China

BAI Jian-chao (1987-), male, native of Shangluo, Shaanxi, associate professor of Northwestern Polytechnical University, engages in numerical algebra and optimization.

Received date: 2024-05-04

Online published: 2025-03-30

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摘要

Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences, we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences. We show that this ratio is solely dependent on the order of the grid, providing a concise and splendid identity.

关键词： Generalized Fibonacci sequence; Fibonacci identity; Odd-order grid; Geometric property

本文引用格式

杨子贤, 白建超 . 广义斐波那契数列在网格中的新性质 [J]. 数学季刊, 2025 , 40(1) : 103 -110 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.010

Abstract

Key words： Generalized Fibonacci sequence; Fibonacci identity; Odd-order grid; Geometric property

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