Determinant representations of sequences

In this talk we recall some recent results concerning (integer) matrices whose leading principal minors formwell-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are many different ways of constructing such matrices. Some of these matrices are con- structed by homogeneous or non-homogeneous recurrence relations, and others are constructed by convolution of two sequences. Here, we will illustrate the idea of some methods by construct- ing some integer matrices of this kind.