  The purpose of this article is to study determinants of matrices which are
known as generalized Pascal triangles (see [1]). We present a factorization by
expressing such a matrix as a product of a unipotent lower triangular matrix, a
Toeplitz matrix and a unipotent upper triangular matrix. The determinant of a
generalized Pascal matrix equals thus the determinant of a Toeplitz matrix.
This equality allows us to evaluate a few determinants of generalized Pascal
matrices associated to certain sequences. In particular, we obtain families of
quasi-Pascal matrices whose principal minors generate any arbitrary linear
subsequences F(nr+s) or L(nr+s), (n=1, 2, 3, ...) of Fibonacci or Lucas
sequence.
