IJPAM: Volume 30, No. 1 (2006)

ON FACTORIZATION OF THE GENERALIZED
FIBONACCI NUMBERS

Jaroslav Seibert$^1$, Pavel Trojovský$^2$
$^{1,2}$Institute of Mathematics
Faculty of Economics and Administration
University of Pardubice
Studentská 84, Pardubice, 532 10, CZECH REPUBLIC
$^2$e-mail: pavel.trojovsky@uhk.cz


Abstract.Several authors gave various factorizations of the Fibonacci and Lucas numbers. In this paper some results on factorizations of the generalized Fibonacci numbers $W_n$ which satisfy the recurrence of the second order $W_{n+2} = pW_{n+1} - qW_n$ are derived. Proofs are made with the help of connections between determinants of tridiagonal matrices and the numbers $W_n$ using the Chebyshev polynomials.

Received: May 24, 2006

AMS Subject Classification: 11B39, 05A15, 05A19

Key Words and Phrases: Fibonacci and Lucas numbers, Chebyshev polynomials, tridiagonal matrices, factorization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 1