scholarly journals A remark about the positivity problem of fourth order linear recurrence sequences

2014 ◽  
Vol 18 (1) ◽  
pp. 3
Author(s):  
Vichian Laohakosol ◽  
Pinthira Tangsupphathawat
Keyword(s):  
Fourth Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Recurrence Sequences

The positivity problem for fourth order linear recurrence sequences is decidable

2012 ◽  
Vol 128 (1) ◽  
pp. 133-142 ◽  
Author(s):  
Pinthira Tangsupphathawat ◽  
Narong Punnim ◽  
Vichian Laohakosol
Keyword(s):  
Fourth Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Recurrence Sequences

scholarly journals Decomposable polynomials in second order linear recurrence sequences

2018 ◽  
Vol 159 (3-4) ◽  
pp. 321-346 ◽  
Author(s):  
Clemens Fuchs ◽  
Christina Karolus ◽  
Dijana Kreso
Keyword(s):  
Second Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Recurrence Sequences

scholarly journals Identities Involving the Fourth-Order Linear Recurrence Sequence

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1476 ◽  
Author(s):  
Lan Qi ◽  
Zhuoyu Chen
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Generating Function ◽  
Fourth Order ◽  
Power Series Expansion ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Order Linear ◽  
Elementary Methods ◽  
Linear Recurrence Sequence

In this paper, we introduce the fourth-order linear recurrence sequence and its generating function and obtain the exact coefficient expression of the power series expansion using elementary methods and symmetric properties of the summation processes. At the same time, we establish some relations involving Tetranacci numbers and give some interesting identities.

scholarly journals General Linear Recurrence Sequences and Their Convolution Formulas

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 132 ◽  
Author(s):  
Paolo Emilio Ricci ◽  
Pierpaolo Natalini
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Second Order ◽  
General Linear ◽  
Linear Recurrence ◽  
Order Linear ◽  
Matrix Polynomials ◽  
Recurrence Sequences ◽  
Straightforward Extension

We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown.

scholarly journals Distribution of some quadratic linear recurrence sequences modulo 1

2014 ◽  
Vol 30 (1) ◽  
pp. 79-86
Author(s):  
ARTURAS DUBICKAS ◽  
Keyword(s):  
Limit Point ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Recurrence Sequences

We show that if a is an even integer then for every ξ ∈ R the smallest limit point of the sequence ||ξan||∞n=1 does not exceed |a|/(2|a| + 2) and this bound is best possible in the sense that for some ξ this constant cannot be improved. Similar (best possible) bound is also obtained for the smallest limit point of the sequence ||ξxn||∞n=1, where (xn)∞n=1 satisfies the second order linear recurrence xn = axn−1 + bxn−2 with a, b ∈ N satisfying a > b. For the Fibonacci sequence (Fn)∞n=1 our result implies that supξ∈R lim infn→∞ ||ξFn|| = 1/5, and e.g., in case when a > 3 is an odd integer, b = 1 and θ := a/2 + p a 2/4 + 1 it shows that supξ∈R lim infn→∞ ||ξθn|| = (a − 1)/2a.

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