On the representation of k sequences of generalized order-k numbers
Number Theory
2011-11-18 v1
Abstract
In this paper, we define k-generalized order-k numbers and we obtain a relation between i-th sequences and k-th sequences of k-generalized order-k numbers. We give some determinantal and permanental representations of k-generalized order-k numbers by using various matrices. Using the relation between i-th sequences and k-th sequences of k-generalized order-k numbers we give some determinantal and permanental representations of i-th sequences of generalized order-k numbers. In addition, we obtain Binet's formula for generalized order-k Pell numbers by using our representations.
Keywords
Cite
@article{arxiv.1111.4057,
title = {On the representation of k sequences of generalized order-k numbers},
author = {Kenan Kaygisiz and Adem Sahin},
journal= {arXiv preprint arXiv:1111.4057},
year = {2011}
}