Determinants of some pentadiagonal matrices - Losonczi, Laszlo (Array, 2021)
In this paper we consider pentadiagonal (n+1)×(n+1) matrices with two subdiagonals and two superdiagonals at distances k and 2k from the main diagonal where 1≤k < 2k n. We give an explicit formula for their determinants and also consider the Toeplitz and "imperfect" Toeplitz versions of such matrices. Imperfectness means that the first and last k elements of the main diagonal differ from the elements in the middle. Using the rearrangement due to Egerv´ary and Sz´asz we also show how these determinants can be factorized.