Journal of Integer Sequences, Vol. 12 (2009), Article 09.8.6

Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays

Paul Barry
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.

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(Concerned with sequences A000045 A000108 A001045 A001405 A001654 A002530 A007318 A008619 A026008 A041011 A049310 A053122 A078812 A084158 A085478 A099025 A109437 A136211 A152119 A157329 A157335 A158909 A165620 A165621.)

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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