Abstract
In this paper, we derive a formula for the generating function of powers of a second-order linear recurrence sequence, with initial conditions 0 and 1. As an example, we find the generating function of the powers of the nonnegative integers. We also find new formulas for computing Eulerian polynomials.
| Original language | English |
|---|---|
| Article number | 18.3.3 |
| Journal | Journal of Integer Sequences |
| Volume | 21 |
| Issue number | 3 |
| State | Published - Jan 1 2018 |
Keywords
- Eulerian polynomial
- Generating function
- Matrix
- Pascal triangle
- Second-order recurrence sequence