广义斐波那契数列在网格中的新性质

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

数学季刊 ›› 2025, Vol. 40 ›› Issue (1): 103-110.doi: 10.13371/j.cnki.chin.q.j.m.2025.01.010

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广义斐波那契数列在网格中的新性质

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

收稿日期:2024-05-04 出版日期:2025-03-30 发布日期:2025-03-30
通讯作者: 白建超 E-mail:bjc1987@163.com
作者简介: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.
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).

A Novel Property of Generalized Fibonacci Sequence in Grids

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

Received:2024-05-04 Online:2025-03-30 Published:2025-03-30
Contact: BAI Jian-chao E-mail:bjc1987@163.com
About author: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.
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).

摘要/Abstract

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

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

中图分类号:

O156.4

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.

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.

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广义斐波那契数列在网格中的新性质

A Novel Property of Generalized Fibonacci Sequence in Grids

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