منابع مشابه
Some Properties of Generalized Third Order Pell Numbers
This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation , 2 , 1 , 0 , 3 , 2 3 , 2 , , = ≥ + = − − m n w w w n m n m m n m , with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the...
متن کاملOn The Usual Fibonacci and Generalized Order-k Pell Numbers
In this paper, we give some relations involving the usual Fibonacci and generalized order-k Pell numbers. These relations show that the generalized order-k Pell numbers can be expressed as the summation of the usual Fibonacci numbers. We nd families of Hessenberg matrices such that the permanents of these matrices are the usual Fibonacci numbers, F2i 1; and their sums. Also extending these mat...
متن کاملTHE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-k PELL NUMBERS
In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the generalized order-k Pell numbers.
متن کاملOn Pell, Pell-Lucas, and balancing numbers
In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.
متن کاملOn the computing of the generalized order-k Pell numbers in log time
In this paper, we consider the generalized order-k Pell numbers and present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves. The theoretical basis of using a matrix method for deriving the algorithm is also discussed. 2006 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Asian Journal of Advanced Research and Reports
سال: 2019
ISSN: 2582-3248
DOI: 10.9734/ajarr/2019/v6i130144