Structural and sparsity properties of symmetric 7-matrices

A matrix A=(aij) is called a 7α,β-matrix if its entries satisfy the recurrence relation αai-1,j-1+βai-1,j=aij, where α and β are fixed nonzero real numbers. In this paper, we study the structural and sparsity properties of symmetric 7α,β-matrices. In particular, we determine the largest number of zero entries of a nonzero 7α,β-matrix and determine the matrices that attain this largest number.