Symmetric third-order recurring sequences, Chebyshev polynomials, and Riordan arrays

We study a family of symmetric third-order recurring sequences with the aid of Riordan arrays and Chebyshev polynomials. Formulas involving both Chebyshev poly-nomials and Fibonacci numbers are established. The family of sequences dened by the product of consecutive terms of the rst family of sequences is also studied, and links to the Chebyshev polynomials are again established, including continued frac-tion expressions. A multiplicative result is established relating Chebyshev polynomials to sequences of doubled Chebyshev polynomials. Links to a special Catalan related Riordan array are explored.