On sequences defined by linear recurrence relations
نویسندگان
چکیده
منابع مشابه
On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or po...
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where a, ai, a2> ■ ■ ■ , a* are given rational integers. The purpose of this paper is to investigate the periodicity of such sequences with respect to a rational integral modulus m. Carmichaelî has studied the period for a modulus m whose prime divisors exceed k and are prime to ak. In this paper, I give a solution to the problem without restriction on m. If m is prime to ak the sequence (1) is...
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A nearly linear recurrence sequence (nlrs) is a complex sequence (an) with the property that there exist complex numbers A0,. . ., Ad−1 such that the sequence ( an+d + Ad−1an+d−1 + · · · + A0an )∞ n=0 is bounded. We give an asymptotic Binet-type formula for such sequences. We compare (an) with a natural linear recurrence sequence (lrs) (ãn) associated with it and prove under certain assumptions...
متن کاملOn the multiplicity of linear recurrence sequences
We prove a lemma regarding the linear independence of certain vectors and use it to improve on a bound due to Schmidt on the zero-multiplicity of linear recurrence sequences. 1 Linear recurrence sequences Let {un}n∈Z be a linear recurrence sequence of complex numbers satisfying the recurrence relation un = c1un−1 + · · ·+ ctun−t, (1) for c1, . . . , ct ∈ C with ct 6= 0. We say it is of order t ...
متن کاملPalindromes in Linear Recurrence Sequences
We prove that for any base b ≥ 2 and for any linear homogeneous recurrence sequence {an}n≥1 satisfying certain conditions, there exits a positive constant c > 0 such that #{n ≤ x : an is palindromic in base b} x1−c.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1931
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1931-1501585-5