Open Access

Extending generalized Fibonacci sequences and their binet-type formula

Advances in Difference Equations20062006:023849

https://doi.org/10.1155/ADE/2006/23849

Received: 8 May 2006

Accepted: 2 July 2006

Published: 14 September 2006

Abstract

We 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.

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Authors’ Affiliations

(1)
Section de Mathématique, LEGT - F. Arago
(2)
Faculty of Mathematics, Kyushu University

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Copyright

© M. Rachidi and O. Saeki 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.