Geodesic
Circulants and the factorization of the Fibonacci–like numbers
Communications in Mathematics, Tome 14 (2006) no. 1, pp. 63-70
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{COMIM_2006_14_1_a9,
     author = {Seibert, Jaroslav and Trojovsk\'y, Pavel},
     title = {Circulants and the factorization of the {Fibonacci{\textendash}like} numbers},
     journal = {Communications in Mathematics},
     pages = {63--70},
     year = {2006},
     volume = {14},
     number = {1},
     mrnumber = {2298915},
     zbl = {1132.11009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a9/}
}
TY  - JOUR
AU  - Seibert, Jaroslav
AU  - Trojovský, Pavel
TI  - Circulants and the factorization of the Fibonacci–like numbers
JO  - Communications in Mathematics
PY  - 2006
SP  - 63
EP  - 70
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a9/
LA  - en
ID  - COMIM_2006_14_1_a9
ER  - 
%0 Journal Article
%A Seibert, Jaroslav
%A Trojovský, Pavel
%T Circulants and the factorization of the Fibonacci–like numbers
%J Communications in Mathematics
%D 2006
%P 63-70
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a9/
%G en
%F COMIM_2006_14_1_a9
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/

[1] Cahill, N. D., D’Errico, J. R., Narayan, D. A. and Narayan, J. Y.: Fibonacci determinants. College Mathematics Journal 33.3 (2002), 221-225.

[2] Cahill, N. D., D’Errico, J. R., Spence, J. P.: Complex factorizations of the Fibonacci and Lucas numbers. The Fibonacci Quarterly 41.1 (2003), 13-19. | MR

[3] Cahill, N. D., Narayan, D. A.: Fibonacci and Lucas numbers as tridiagonal matrix determinants. The Fibonacci Quarterly 42.2 (2004), 216-221. | MR

[4] Gradshteyn, J. S., Ryzhik, I. M.: Tables of Integrals, Series and Products. 5th ed. San Diego, CA: Academic Press, 1979.

[5] Horadam, A. F.: Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence–generated sequences. The Fibonacci Quarterly 26.2 (1988), 98-114. | MR | Zbl