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Trigonometric factorizations of the Horadam sequence and its companion sequence

We consider the Horadam sequence and its companion sequence 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.