منابع مشابه
The generalized order-k Fibonacci–Pell sequence by matrix methods
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 me...
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In this paper, and from the definition of a distance between numbers by a recurrence relation, new kinds of k–Fibonacci numbers are obtained. But these sequences differ among themselves not only by the value of the natural number k but also according to the value of a new parameter r involved in the definition of this distance. Finally, various properties of these numbers are studied.
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In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.
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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...
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In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00553-6