Some combinatorial identities via Fibonacci numbers

Singular Case of Generalized Fibonacci and Lucas Matrices

“…In this section we want to investigate correlation between the matrix F (a,b,−1) n and Pascal matrices. Since rank(F (a,b,−1) n ) = n−1 and rank(P n ) = n, it is not possible to use P n in the usual manner as in [23], [32], [21]. For this purpose we introduce the following definition of Pascal matrices of type s. …”

A factorization of the symmetric Pascal matrix involving the Fibonacci matrix

“…The inverse of F n was also given as follows: In fact, formula (3) is an immediate consequence of the isomorphism between lower formal power series and lower triangular Toeplitz matrices. In [5], Lee et al obtained the following result:…”

“…In this short note, we give a second factorization of the Pascal matrix which was apparently missed by the authors in [5].…”

On Fibo-Pascal Matrix Involving k-Fibonacci and k-Pell Matrices

“…Pascal matrices, binomial coefficients, Fibonomial coefficients, F-nomial coefficients, their generalizations and factorizations are studied by many authors [2,3,[7][8][9][10][11][12]14,[18][19][20][21].…”