Binary words excluding a pattern and proper Riordan arrays

We study the relation between binary words excluding a pattern and proper Riordan arrays. In particular, we prove necessary and sufficient conditions under which the number of words counted with respect to the number of zeroes and ones bits are related to proper Riordan arrays. We also give formulas for computing the generating functions (d(x),h(x))(d(x),h(x)) defining the Riordan array.