A note on linear recursions. Issue 1 (31st December 2023) - Wananiyakul, Saeree; Tongsomporn, Janyarak
Abstract: We consider linear recursions of length two and related gap recursions where the indices may not be consecutive integers. Given a linear recursion of length two, we prove the existence of an explicit linear recursion of length l with arbitrary distance between indices. Conversely, it is shown under some mild assumption that a linear recursion of length l can be reduced to one of length two.