Determinant Representations of Sequences: A Survey

Abstract

This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this type.

Keywords

• determinant
• generalized pascal triangle
• (quasi) toeplitz matrix
• (quasi) pascal-like matrix
• fibonacci (lucas
• jacobsthal and pell) sequence