Advances in Difference Equations
Volume 2006 (2006), Article ID 23849, 11 pages
doi:10.1155/ADE/2006/23849
Extending generalized Fibonacci sequences and their Binet-type formula
Mustapha Rachidi1
and Osamu Saeki2
1Section de Mathématique, LEGT - F. Arago, Académie de Reims, 1, rue F. Arago, Reims 51100, France
2Faculty of Mathematics, Kyushu University, Hakozaki 812-8581, Fukuoka, Japan
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.