Abstract
Hoggatt and Bergum [2] studied the general expression for the entry in the ith row and the jth column of a convolution matrix and obtained row generating functions for the convolution matrix of the sequence {1, u2, u3, u4, ...}. In this paper, we extend the Strong Convolution Decomposition Theorem [3] to a more general case. Based on this extension, we decompose a convolution matrix into a product of a lower trianglular matrix and the upper triangular Pascallike matrix. This interesting decomposition of a convolution matrix leads a novel approach to the subject proposed in [2] . Using this new method, we obtain a simple explicit formula for entries of a convolution matrix and row generating functions of the convolution matrix of the sequences {vn} and {un}. Moreover, the approach developed here can be easily extended to a rather broad category of integer matrices.