Add to ORKGWe study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence. We also study infinite order recurrence relations in a strong sense and give a complete answer to the extension problem. We also obtain a Binet-type formula, answering several open questions about these sequences and their characteristic power series. Copyright © 2006 M. Rachidi and O. Saeki. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distri-bution, and reproduction in any medium, provided the original work is properly cited. 1
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
Let {ai, j} be real numbers for 0 ≤ i ≤ r - 1 and 1 ≤ j ≤ 2, and define a sequence {vn} with initial...
The sequence of Fibonacci numbers is defined by F0 = 0, Fj = 1, and F 9 = F + n+2 n F,- (n ^ 0), and...
summary:The Pell sequence $(P_n)_{n=0}^{\infty }$ is the second order linear recurrence defined by $...
AbstractIn this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences,...
Copyright © 2014 Mamta Singh et al. This is an open access article distributed under the Creative Co...
summary:The Pell sequence $(P_n)_{n=0}^{\infty }$ is the second order linear recurrence defined by $...
Abstract In this study, we present certain properties of Generalized Fibonacci sequence. Generalized...
Abstract The Fibonacci sequence, Lucas numbers and their generalization have many interesting proper...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
This paper considers some properties of types of recurrence relations which generalize the well-know...
Fibonacci sequence is a well known example of second order linear recurrence relatio. Besides Fibona...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
WOS: 000329081500003In this study, we define a generalization of Lucas sequence {p(n)}. Then we obta...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
Let {ai, j} be real numbers for 0 ≤ i ≤ r - 1 and 1 ≤ j ≤ 2, and define a sequence {vn} with initial...
The sequence of Fibonacci numbers is defined by F0 = 0, Fj = 1, and F 9 = F + n+2 n F,- (n ^ 0), and...
summary:The Pell sequence $(P_n)_{n=0}^{\infty }$ is the second order linear recurrence defined by $...
AbstractIn this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences,...
Copyright © 2014 Mamta Singh et al. This is an open access article distributed under the Creative Co...
summary:The Pell sequence $(P_n)_{n=0}^{\infty }$ is the second order linear recurrence defined by $...
Abstract In this study, we present certain properties of Generalized Fibonacci sequence. Generalized...
Abstract The Fibonacci sequence, Lucas numbers and their generalization have many interesting proper...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
This paper considers some properties of types of recurrence relations which generalize the well-know...
Fibonacci sequence is a well known example of second order linear recurrence relatio. Besides Fibona...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
WOS: 000329081500003In this study, we define a generalization of Lucas sequence {p(n)}. Then we obta...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
Let {ai, j} be real numbers for 0 ≤ i ≤ r - 1 and 1 ≤ j ≤ 2, and define a sequence {vn} with initial...
The sequence of Fibonacci numbers is defined by F0 = 0, Fj = 1, and F 9 = F + n+2 n F,- (n ^ 0), and...