On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0 kW3 k and Σn k=1 kW3− k
نویسندگان
چکیده
منابع مشابه
Generalized (k, r)–Fibonacci Numbers
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 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
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In this paper, we consider the relationships between the sums of the generalized order-k Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction We consider the generalized order k Fibonacci and Lucas numbers. In [1], Er de ned k sequences of the generalized order k Fibonacci numbers as shown: g n = k X j=1 g n j ; for n > 0 and 1 i k; (1.1) with boundary conditions for 1...
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In this paper, we give formulas for the sums of generalized order-k Fibonacci, Pell and similar other sequences which we obtain using matrix methods. As applications, we give explicit formulas for the Tribonacci and Tetranacci numbers. 1. Introduction The well-known Fibonacci sequence fFng is de ned for n > 2 by Fn+1 = Fn + Fn 1 where F1 = F2 = 1: The well-known Pell sequence fPng is de ned for...
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ژورنال
عنوان ژورنال: Asian Research Journal of Mathematics
سال: 2020
ISSN: 2456-477X
DOI: 10.9734/arjom/2020/v16i630196