Matrices determined by a linear recurrence relation among entries

Abstract

A matrix A=[ a ij ] is called a 7-matrix if its entries satisfy the recurrence relation αa i−1, j−1 + βa i−1, j = a ij where α, β are fixed numbers. A 7-matrix is completely determined by its first row and first column. In this paper we determine the structure of 7-matrices and investigate the sequences represented by columns of infinite 7-matrices.