A closed formula for linear recurrences with constant coefficients
Glenn Bruda, Bruce Fang, Pico Gilman, Raul Marquez, Steven J. Miller, Beni Prapashtica, Daeyoung Son, Saad Waheed, Janine Wang
公開日: 2024/8/22
Abstract
Given a linear recurrence of the form $c_n=a_1c_{n-1}+\cdots+a_j c_{n-j}$, it is well-known that $c_n=\sum_{r}p_r(n)r^n$, where the sum is taken over the set of characteristic roots and each $p_r(n)$ is some polynomial. We give a closed formula for the coefficients of each polynomial $p_r(n)$ for any linear recurrence of this form.