A closed formula for linear recurrences with constant coefficients
A closed formula for linear recurrences with constant coefficients
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.
Glenn Bruda、Bruce Fang、Pico Gilman、Raul Marquez、Steven J. Miller、Beni Prapashtica、Daeyoung Son、Saad Waheed、Janine Wang
数学
Glenn Bruda,Bruce Fang,Pico Gilman,Raul Marquez,Steven J. Miller,Beni Prapashtica,Daeyoung Son,Saad Waheed,Janine Wang.A closed formula for linear recurrences with constant coefficients[EB/OL].(2025-09-01)[2025-09-05].https://arxiv.org/abs/2408.12660.点此复制
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