Sequence characterization of almost Riordan arrays

A lot of research has been done on Riordan arrays. Some of these studies have given generalizations and different forms of Riordan arrays. In this thesis, almost-Riordan arrays, that are one of the different forms of Riordan arrays, are taken into consideration. Sequence characterizations of almost-Riordan arrays are given by considering the generating functions of $A$, $Z$ and $\omega-$ sequences of the almost Riordan arrays. In addition, the sequence characterizations of the inverse of the almost-Riordan arrays and product of two almost-Riordan arrays are obtained. In the last part of the thesis, another characterization of almost-Riordan arrays is obtained by considering the generating functions of row sum, alternating row sum and weighted row sum of the almost-Riordan arrays.