منابع مشابه
New 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 ...
متن کاملTernary Modified Collatz Sequences And Jacobsthal Numbers
We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...
متن کاملJacobsthal numbers in generalised Petersen graphs
We prove that the number of 1-factorisations of a generalised Petersen graph of the type GP (3k, k) is equal to the kth Jacobsthal number J(k) if k is odd, and equal to 4J(k), when k is even. Moreover, we verify the list colouring conjecture for GP (3k, k).
متن کاملSome 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.
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ژورنال
عنوان ژورنال: Asian Research Journal of Mathematics
سال: 2019
ISSN: 2456-477X
DOI: 10.9734/arjom/2019/v15i430153