Identities on the New Generalizations of Fibonacci and Lucas Sequences
Abstract
In this paper, we introduced the sequences and which are defined by the recurrence relations and for positive integer with initial conditions, and respectively, where and are positive real numbers and. We study the generating functions, Binet’s formulas. Moreover, we also provide generalized identities of and by using Binet’s formulas for derivation. Keywords : Fibonacci sequence, Lucas sequence, generating functions, Binet’s formulasReferences
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29(8), 1429-1437.
Edson, M. and Yayenie, O. (2009). A new generalization of Fibonacci sequences and extended binet formula.
Intergers, 9, 639-654.
Edson, M., Lewis, S. and Yayenie, O. (2011). The k-Periodic Fibonacci sequences and extended binet
formula. Intergers, 11, 739-751.
Falcon, S. and Plaza, A. (2007).The k-Fibonacci sequence and pascal 2- triangle. Chaos, Solitons and
Fractals, 33, 38-49.
Horadam, A.F. (1961). A generalized of Fibonacci sequences. Amer. Math. Monthly, 68, 455-459.
Klein, S.T. (1991). Combinatorial Representation of generalized Fibonacci numbers. Fibonacci Quarterly,
29, 124-131.
Melham, R.S. and Shannon, A.G. (1995). A generalization of the Catalan identity and some consequences.
Fibonacci Quarterly, 33, 82-84.
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2018-11-21
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บทความวิจัยจากการประชุมวิชาการระดับชาติ"วิทยาศาสตร์วิจัย"ครั้งที่ 10
