The Generalized Order-K Fibonacci-Pell Sequence by Matrix Methods

Abstract

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.