Analysis of a Third Order Non-linear Recurrence including Exponential and Factorial terms

This paper investigates a specific third-order nonlinear recurrence sequence. Despite the presence of super-exponential growth driven by factorial and exponential terms, numerical analysis confirms that the sequence remains periodic for modulo m up to 1000 as checked yet, suggesting that it might be periodic further too. Excel files for period lengths and terms of sequence are attached along with python codes used to generate period lengths and terms本文研究一类特定的三阶非线性递推序列。尽管该序列由阶乘项与指数项驱动，呈现超指数增长，但数值分析结果证实，截至目前已验证的模m（最大至1000）下，该序列仍保持周期性，这暗示其在更大模值下或许同样具备周期性。本文附带了存储该序列周期长度与序列项的Excel文件，以及用于生成该序列周期长度与序列项的Python代码。