Matrices determined by a linear recurrence relation among entries

A matrix A=[aij] is called a 7-matrix if its entries satisfy the recurrence relation αai−1,j−1+βai−1,j=aij 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.