Determinant of Three-Layer Toeplitz Matrices
Institute of Physics and Mathematics
Komi Science Centre UrD RAS
Kommunisticheskaya Street 24
We obtain an explicit and efficient formula for the determinant of a
three-layer Toeplitz matrix. We show that many well-known sequences, such
as Jacobsthal numbers, generalized Fibonacci numbers, and k-Fibonacci
numbers, can be represented as sequences of determinants of three-layer
Toeplitz matrices. Further, we evaluate the spectrum for one of these
matrices using the obtained formulae and, as a consequence, discover
some interesting factorizations of certain integer sequences in terms of
products of complex numbers, the imaginary parts of which are expressed
using the tangent function.
Full version: pdf,
(Concerned with sequences
Received June 10 2021; revised version received August 20 2021.
Published in Journal of Integer Sequences,
October 25 2021.
Journal of Integer Sequences home page