Some generalizations of the Jacobsthal numbers
نویسندگان
چکیده
منابع مشابه
Some Generalizations of the Jacobsthal Numbers
The main object of this paper is to introduce and investigate some properties and relations involving sequences of numbers Fn,m(r), for m = 2, 3, 4, and r is some real number. These sequences are generalizations of the Jacobsthal and Jacobsthal Lucas numbers.
متن کاملOn Some Identities of k-Jacobsthal-Lucas Numbers
In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83
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Around 1778 Euler discovered a method by which he could use certain numbers to find large primes. However, not every number is suitable for this method and hence he gave the name numeri idonei (= suitable, convenient numbers) to those numbers that are suitable. Gauss also considered idoneal numbers from a related but slightly different point of view. After Gauss, many people considered idoneal ...
متن کاملNew families of Jacobsthal and Jacobsthal-Lucas numbers
In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. Introduction Several sequences of positive integers were and still are object of study for many researchers. Examples of these sequences are the well known Fibonacci ...
متن کاملA New Generalization of Jacobsthal Numbers (bi-periodic Jacobsthal Sequences)
The bi-periodic Fibonacci sequence also known as the generalized Fibonacci sequence was fırst introduced into literature in 2009 by Edson and Yayenie [9] after which the bi-periodic Lucas sequence was defined in a similar fashion in 2004 by Bilgici [5]. In this study, we introduce a new generalization of the Jacobsthal numbers which we shall call bi-periodic Jacobsthal sequences similar to the ...
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ژورنال
عنوان ژورنال: Filomat
سال: 2010
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1002143d