Trigonometric factorizations of the Horadam sequence and its companion sequence

Z. Siar

Bingöl University, Faculty of Arts and Sciences, Department of Mathematics, Turkey

Abstract: 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, tridiagonal matrix, eigenvalue.

UDC: 512.643+517.962.27

MSC: 11B39, 11C20, 15B05, 15A18

Received: 22.03.2017
Revised: 27.03.2018

DOI: 10.4213/im8676

 English version: Izvestiya: Mathematics, 2018, 82:6, 1265–1277

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