Geodesic
Trigonometric factorizations of the Horadam sequence and its companion sequence
Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1265-1277

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We consider the Horadam sequence $\{W_n\}$ and its companion sequence $\{X_n\}$ satisfying a second-order recurrence. We generalize earlier results by giving new results about factorizations of these sequences. In order to obtain these results, we use connections between the determinants of tridiagonal matrices and the terms of these sequences, and also take advantage of Chebyshev polynomials of the second kind.
Keywords: Horadam sequence, determinant, eigenvalue.
Mots-clés : tridiagonal matrix 
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     author = {Z. Siar},
     title = {Trigonometric factorizations of the {Horadam} sequence and its companion sequence},
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Z. Siar. Trigonometric factorizations of the Horadam sequence and its companion sequence. Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1265-1277. http://geodesic.mathdoc.fr/item/IM2_2018_82_6_a7/