The generalized order-k Fibonacci-Pell sequence by matrix methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:209

Article

Kilic, Emrah

关键词: generalized Fibonacci and Pell number;    sums;    generating function;    matrix methods;   

DOI  :  10.1016/j.cam.2006.10.071

来源: Elsevier

【 摘 要 】

In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, then we define a new recurrence, which we call generalized order-k F-P sequence. Also we present a systematic investigation of the generalized order-k F-P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F-P sequence by matrix methods. Further, we give the generating function and combinatorial representations of these numbers. Also we present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves. (C) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free