Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays
School of Science
Waterford Institute of Technology
We study a family of symmetric third-order recurring sequences with the
aid of Riordan arrays and Chebyshev polynomials. Formulas involving
both Chebyshev polynomials and Fibonacci numbers are established. The
family of sequences defined by the product of consecutive terms of the
first family of sequences is also studied, and links to the Chebyshev
polynomials are again established, including continued fraction
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.
Full version: pdf,
(Concerned with sequences
Received February 27 2009;
revised versions received March 30 2009; June 8 2009; December 3 2009.
Published in Journal of Integer Sequences, December 3 2009.
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