Geodesic
Symmetric third-order recurring sequences, Chebyshev polynomials, and Riordan arrays
Journal of integer sequences, Tome 12 (2009) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 11B83, 11A55, 11B37, 11Y55, 33C45
Keywords: integer sequence, linear recurrence, riordan arrays, Chebyshev polynomials, continued fraction 
@article{JIS_2009__12_8_a5,
     author = {Barry, Paul},
     title = {Symmetric third-order recurring sequences, {Chebyshev} polynomials, and {Riordan} arrays},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {12},
     number = {8},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a5/}
}
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Barry, Paul. Symmetric third-order recurring sequences, Chebyshev polynomials, and Riordan arrays. Journal of integer sequences, Tome 12 (2009) no. 8. http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a5/