A Note on Derived Linear Recurring Sequences*

Abstract

A linear recurring sequence u ₀, u ₁ u ₂, …} of kth order over Q, the field of rational numbers, is defined by the recurrence

$$ {{u}_{{n + k}}} = \sum\limits_{{i = 1}}^{k} {{{{( - 1)}}^{{i - 1}}}{{\sigma }_{i}}{{u}_{{n + k - i}}}{{\sigma }_{i}} \in \mathbb{Q}} $$

(1)

The sequence u _n can be nicely characterized, [2, Vol. I, p. 410], by determinants that define derived sequences.

This research was partially supported by CNR