A note on the sequence of A. F. Horadam.
Udrea, Gheorghe (1996)
Portugaliae Mathematica
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Udrea, Gheorghe (1996)
Portugaliae Mathematica
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Udrea, Gheorghe (1998)
Portugaliae Mathematica
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Udrea, Gheorghe (1998)
Portugaliae Mathematica
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Wituła, Roman (2009)
Journal of Integer Sequences [electronic only]
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Chatterjea, S.K., Eaqub Ali, S.M. (1991)
International Journal of Mathematics and Mathematical Sciences
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Mihoubi, Miloud, Maamra, Mohammed Said (2011)
Journal of Integer Sequences [electronic only]
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Gregorac, R.J. (1989)
International Journal of Mathematics and Mathematical Sciences
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Toma, Ghiocel (2010)
Mathematical Problems in Engineering
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Huang, Fengying, Liu, Bolian (2010)
The Electronic Journal of Combinatorics [electronic only]
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Jaroslav Seibert, Pavel Trojovský (2006)
Acta Mathematica Universitatis Ostraviensis
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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 and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
Rosema, S.W., Tijdeman, R. (2005)
Integers
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Juan Varona (2006)
Open Mathematics
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We give a short proof to characterize the cases when arccos(√r), the arccosine of the squareroot of a rational number r ∈ [0, 1], is a rational multiple of π: This happens exactly if r is an integer multiple of 1/4. The proof relies on the well-known recurrence relation for the Chebyshev polynomials of the first kind.