Chinese Quarterly Journal of Mathematics >

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

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

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
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.
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

Supported by

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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Abstract

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.

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

Cite this article

YANG Zi-xian, BAI Jian-chao . A Novel Property of Generalized Fibonacci Sequence in Grids[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(1) : 103 -110 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.010

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