More Identities and Tridiagonal Matrices About Fibonacci and Lucas Numbers

Abstract

In this paper, we derive a family of identities on the arbitrary subscripted Fibonacci and Lucas numbers. Furthermore, we construct the tridiagonal and symmetric tridiagonal family of matrices whose determinants form any linear subsequence of the Fibonacci numbers and Lucas numbers. Thus, we give a generalization of the results presented in Nalli and Civciv [A. Nalli, H. Civciv, A generalization of tridiagonal matrix determinants, Fibonacci and Lucas numbers, Chaos, Solitons and Fractals \(2009;40(1):355 .61]\) and Cahill and Narayan [N. D. Cahill, D. A. Narayan, Fibonacci and Lucas numbers as tridiagonal matrix determinants, The Fibonacci Quarterly, \(2004;42(1):216–221]\).