IJPAM: Volume 107, No. 4 (2016)

ON DETERMINANTS OF TRIDIAGONAL MATRICES WITH
ALTERNATING PAIRS OF $1^{\prime }s$ AND $-1^{\prime }s$ ON THE DIAGONAL
CONNECTED WITH FIBONACCI NUMBERS

Pavel Trojovský
Department of Mathematics
University of Hradec Králové
Rokitanského 62
50003 Hradec Králové, CZECH REPUBLIC


Abstract. We will concentrate on some special tridiagonal matrices connected with Fibonacci numbers. In the previous paper we generalized one of the results in Strang's book, as we derived that determinants of some tridiagonal matrices with alternating $1^{\prime }s$ and $-1^{\prime }s$ on the diagonal or the superdiagonal are connected with Fibonacci numbers. This paper is devoted to a generalization of that paper, we show determinants of tridiagonal matrices with alternating pairs of $1^{\prime }s$ and $% -1^{\prime }s$ on the diagonal are related to Fibonacci numbers too.

Received: February 7, 2016

AMS Subject Classification: 11B39, 11B36, 11A07

Key Words and Phrases: tridiagonal matrix, recurrence, Fibonacci number, determinant

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DOI: 10.12732/ijpam.v107i4.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 4
Pages: 903 - 908


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