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

Paul Barry

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1 Citation (Scopus)


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 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.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalJournal of Integer Sequences
Issue number8
Publication statusPublished - 2009


  • Chebyshev polynomials
  • Continued fraction
  • Integer sequence
  • Linear recurrence
  • Riordan arrays


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