Geodesic
Circulants and the factorization of the Fibonacci–like numbers
Communications in Mathematics, Tome 14 (2006) no. 1, pp. 63-70

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MR Zbl
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
Classification : 05A15, 05A19, 11B39
Keywords: Fibonacci and Lucas numbers; tridiagonal matrix; circulant 
Seibert, Jaroslav; Trojovský, Pavel. Circulants and the factorization of the Fibonacci–like numbers. Communications in Mathematics, Tome 14 (2006) no. 1, pp. 63-70. http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a9/
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