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Linearlization of generalized Fibonacci sequences
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In this paper, we give linearization of generalized Fibonacci sequences {gn} and {qn}, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {gn} and {qn}, respectively. Then we re-prove the Cassini's identity for {gn} and {qn}, respectively.
Abstract
In this paper, we give linearization of generalized Fibonacci sequences {gn} and {qn}, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {gn} and {qn}, respectively. Then we re-prove the Cassini's identity for {gn} and {qn}, respectively.
참고문헌 (12)
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- R. J. Hendel, "Approaches to the formula for nth Fibonacci number", College Math. J, 25, pp.139~142 (1994)
- S. Ikikardes, "Some properties of the generalized Fibonacci and Lucas sequences related to the extended Hecke groups", Journal of Inequalities and Applications, pp.398~ (2013)
- D. Kalman, "The Fibonacci numbers - Exposed", The Mathematical Magazine 2, ~ (2002)
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- J. R. Silvester, "Fibonacci properties by matrix methods", Mathematical Gazette, 63, pp.188~191 (1979)
- B. Singh, "Fibonacci-Like sequence and its properties", Int. J. Contemp. Math. Sciences, 5(18), pp.895~868 (2010)
- D. Vella, "Cycles in the Generalized Fibonacci Sequence modulo a Prime", The Mathematical Magazine, 75(4), pp.294~299 (2002)
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