In the present paper, we evaluate the permanent and determinant of some Toeplitz-Hessenberg matrices with generalized Fibonacci and generalized Lucas numbers as entries.We develop identities involving sums of products of generalized Fibonacci numbers and generalized Lucas numbers with multinomial coefficients using the matrix structure, and then we present an application of the determinant of such matrices.
Belbachir, Hacène; Belkhir, Amine; and Djellas, Ihab-Eddine
(R1979) Permanent of Toeplitz-Hessenberg Matrices with Generalized Fibonacci and Lucas entries,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
2, Article 15.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss2/15