Power sums in hyperbolic Pascal triangles

In this paper, we describe a method to determine the power sum of the elements of the rows in the hyperbolic Pascal triangles corresponding to –4, q} with q ≥ 5. The method is based on the theory of linear recurrences, and the results are demonstrated by evaluating the k^th power sum in the range 2 ≤ k ≤ 11.