The generalized order-k Fibonacci–Pell sequence by matrix methods
نویسنده
چکیده
In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, thenwe 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. © 2006 Elsevier B.V. All rights reserved. MSC: 11B37; 11C20; 15A18; 05A15
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