Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences
نویسندگان
چکیده
منابع مشابه
Some Identities for Generalized Fibonacci and Lucas Sequences
In this study, we define a generalization of Lucas sequence {pn}. Then we obtain Binet formula of sequence {pn} . Also, we investigate relationships between generalized Fibonacci and Lucas sequences.
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Horadam [7], in a recent article, defined two sequences of polynomials Jn(x) and j„(x), the Jacobsthal and Jacobsthal-Lucas polynomials, respectively, and studied their properties. In the same article, he also defined and studied the properties of the rising and descending polynomials i^(x), rn(x), Dn(x)y and dn(x), which are fashioned in a manner similar to those for Chebyshev, Fermat, and oth...
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We define the convolved hðxÞ-Fibonacci polynomials as an extension of the classical con-volved Fibonacci numbers. Then we give some combinatorial formulas involving the hðxÞ-Fibonacci and hðxÞ-Lucas polynomials. Moreover we obtain the convolved hðxÞ-Fibo-nacci polynomials from a family of Hessenberg matrices. Fibonacci numbers and their generalizations have many interesting properties and appli...
متن کاملOn Fibonacci-Like Sequences
In this note, we study Fibonacci-like sequences that are defined by the recurrence Sk = a, Sk+1 = b, Sn+2 ≡ Sn+1 + Sn (mod n + 2) for all n ≥ k, where k, a, b ∈ N, 0 ≤ a < k, 0 ≤ b < k + 1, and (a, b) 6= (0, 0). We will show that the number α = 0.SkSk+1Sk+2 · · · is irrational. We also propose a conjecture on the pattern of the sequence {Sn}n≥k.
متن کاملOn Periodic ∞-generalized Fibonacci Sequences
The notion of an∞-generalized Fibonacci sequence has been introduced in [6], and studied in [1], [7], [9]. This class of sequences defined by linear recurrences of infinite order is an extension of the class of ordinary (weighted) r-generalized Fibonacci sequences (r-GFS, for short) with r finite defined by linear recurrences of r order (for example, see [2], [3], [4], [5], [8] etc.) More preci...
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2016
ISSN: 2333-1100
DOI: 10.12691/tjant-2-6-9