A generalization of tridiagonal matrix determinants, Fibonacci and Lucas numbers

Ayşe Nalli and Haci Civciv

Chaos, Solitons & Fractals, 2009, vol. 40, issue 1, 355-361

Abstract: In this paper, we construct the symmetric tridiagonal family of matrices M-α,-β(k),k=1,2,… whose determinants form any linear subsequence of the Fibonacci numbers. Furthermore, we construct the symmetric tridiagonal family of matrices T-α,-β(k),k=1,2,… whose determinants form any linear subsequence of the Lucas numbers. Thus we give a generalization of the presented in Cahill and Narayan (2004) [Cahill ND, Narayan DA. Fibonacci and Lucas numbers as tridiagonal matrix determinants. Fibonacci Quart 2004;42(3):216–21].

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:1:p:355-361

DOI: 10.1016/j.chaos.2007.07.069

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