# Power sums in hyperbolic Pascal triangles

## TL;DR

This paper introduces a linear recurrence-based method to compute power sums of elements in hyperbolic Pascal triangles for specific parameters, demonstrating the approach by calculating sums for powers 2 through 11.

## Contribution

It presents a novel method using linear recurrences to determine power sums in hyperbolic Pascal triangles with parameters 4,q for q5, expanding computational techniques in this area.

## Key findings

- Method successfully computes power sums for 2  k  11.
- Provides explicit formulas for power sums in hyperbolic Pascal triangles.
- Demonstrates the method's effectiveness through concrete calculations.

## Abstract

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 $q\ge5$. 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 $2\le k\le 11$.