On the duals of the Fibonacci and Catalan-Fibonacci polynomials and Motzkin paths

25 Jan 2021 · Paul Barry ·

We use the inversion of coefficient arrays to define dual polynomials to the Fibonacci and Catalan-Fibonacci polynomials, and we explore the properties of these new polynomials sequences. Many of the arrays involved are Riordan arrays. Direct links to the counting of Motzkin paths by different statistics emerge.