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