Abstract This paper investigates a specific family of linear recurrent sequences characterized by a single negative coefficient at the first preceding term. It is shown that the characteristic polynomials of such systems possess a unique property: as the order of the system increases, the moduli of their dominant roots monotonically converge to √2 This result contrasts with classical cases, such as Pisot numbers, where the limit is 2. The findings are supported by high-precision numerical calculations and an analytical derivation.
Emma Helmdach (Fri,) studied this question.
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