A generalised recurrence relation for irrational powers

In previous issues of Parabola, Randell Heyman showed that $c_n = (1 + \sqrt{2})^n + (1 - \sqrt{2})^n$ is an integer for each natural number $n$ and Xiaoyan Hu derived a recursion relation for this sequence. This article extends upon these results, by providing another method to arrive at the recursive relation.