A Novel Property of Generalized Fibonacci Sequence in Grids  

广义斐波那契数列在网格中的新性质

作　　者：YANG Zi-xian BAI Jian-chao 杨子贤;白建超

机构地区：[1]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710129,China

出　　处：《Chinese Quarterly Journal of Mathematics》2025年第1期103-110,共8页数学季刊(英文版)

基　　金：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);the Shaanxi Province College Student Innovation and Entrepreneurship Training Program(Grant Nos.S202210699481 and S202310699324X).

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 

分 类 号：O156.4[理学—数学]