Half Riordan Array Sequences

Abstract We construct sequences of vertical and horizontal halves of various Riordan arrays by using the vertical and horizontal halve Riordan array transform operators. The sequence characterizations of halves of Riordan arrays are presented and applied to the halve Riordan array transformation. The conditions of transforming a Riordan array to a pseudo-involution Riordan array by using the halve Riordan array transform are given. The condition of preserving the elements of a certain subgroup of the Riordan group under the halve Riordan array transformation are shown. Other properties of the halves of Riordan arrays and their entries such as related recurrence relations, double variable generating functions, combinatorial interpretations are also studied.