Circulants and the factorization of the Fibonacci-like numbers. (English) Zbl 1132.11009

Using circulant matrices, their determinants and eigenvalues the authors give factorizations of the Fibonacci-like numbers \(U_n\) and their squares \(U^2_n\). \(U_n\) is defined by \(U_n= pU_{n-1}+ qU_{n-2}\), \(n\geq 2\), \(U_0= 0\), \(U_1= 1\) and arbitrary integers \(p\), \(q\).


11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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[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. · Zbl 1046.11007
[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. · Zbl 1056.11005
[3] Cahill, N. D., Narayan, D. A.: Fibonacci and Lucas numbers as tridiagonal matrix determinants. The Fibonacci Quarterly 42.2 (2004), 216-221. · Zbl 1080.11014
[4] Gradshteyn, J. S., Ryzhik, I. M.: Tables of Integrals, Series and Products. 5th San Diego, CA: Academic Press, 1979. · Zbl 0981.65001
[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. · Zbl 0647.10014
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