On Determinants of Tridiagonal Matrices With Alternating Pairs of 1' and -1' on the Diagonal Connected With Fibonacci Numbers

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 ′ s and −1 ′ 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 ′ s and −1 ′ s on the diagonal are related to Fibonacci numbers too.

ON A SEQUENCE OF ($i$, $\pm 1,$ $\pm i$)-TRIDIAGONAL MATRICES, WHOSE DETERMINANTS ARE RELATED TO FIBONACCI NUMBERS

“…Many authors derived the similar types of matrices which determinants or permanents are related to Fibonacci numbers or different kinds of their generalizations, e. g. k-generalized Fibonacci numbers, see [2], [3], [4], [5], [6], [8], [9], [10], [13], [14], [15] and [16]. Now we turn our attention to the relation of determinants of special tridiagonal matrices with Fibonacci numbers.…”