Half of a Riordan array and restricted lattice paths

For an infinite lower triangular matrix G=(gn,k)n,k≥0, we define the half of G to be the infinite lower triangular matrix H=(hn,k)n,k≥0 such that hn,k=g2n−k,n for all n≥k≥0. In this paper, we will show that if G=(gn,k)n,k≥0 is a Riordan array, then its half H=(hn,k)n,k≥0 is also a Riordan array, and we obtain new combinatorial interpretations for some Riordan arrays in terms of weighted lattice paths.