  Riordan arrays, denoted by pairs of generating functions (g(z), f(z)), are
infinite lower-triangular matrices that are used as combinatorial tools. In
this paper, we present Riordan and stochastic Riordan arrays that have
connections to the Fibonacci and modified Lucas numbers. Then, we present some
pseudo-involutions in the Riordan group that are based on constructions
starting with a certain generating function g(z). We also present a theorem
that shows how to construct pseudo-involutions in the Riordan group starting
with a certain generating function f(z) whose additive inverse has
compositional order 2. The theorem is then used to construct more
pseudo-involutions in the Riordan group where some arrays have connections to
the Fibonacci and modified Lucas numbers. A MATLAB algorithm for constructing
the pseudo-involutions is also given.
