Results 111 to 120 of about 31,545 (292)
Some infinite series summations involving linear recurrence relations of order 2 and 3 [PDF]
Notes on Number Theory and Discrete MathematicsThis paper extends known results of second and third order recursive sequences through extensive formulations of properties of the roots of their characteristic equations, some are old but most are new. They are applied to novel studies of Σₙ₌ₒ^∞ aₘₙ/10ⁿ⁺
Anthony G. Shannon +4 more
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On the Lucas Difference Sequence Spaces Defined by Modulus Function
, 2019 In this paper, firstly, we define the Lucas difference sequence spaces by the help of Lucas sequence and a sequence of modulus function. Besides, we give some inclusion relations and examine geometrical properties such as Banach-Saks type p, weak fixed ...
Karakaş, Ayşe M. +2 more
core
ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS [PDF]
Journal of the Korean Mathematical Society, 2005 The sequences \(\{U_n\}_{n\geq 0}\) and \(\{V_n\}_{n\geq 0}\) are introduced by recurrence relations: \[ \begin{aligned} U_n &= (q- 2)(U_{n-2}- U_{n-4},\;n\geq 4,\\ V_n &= (q-2) V_{n-2}- V_{n-4},\;n\geq 4\end{aligned} \] with initial conditions \(U_0= 0\), \(U_1= 1\), \(U_2= 1\), \(U_4= q- 1\), \(V_0= 2\), \(V_1= 1\), \(V_2= q-1\), where \(q\geq 5\) is
openaire +4 more sources
A dynamical property unique to the Lucas sequence
, 2001 The only recurrence sequence satisfying the Fibonacci recurrence and realizable as the number of periodic points of a map is (a multiple of) the Lucas ...
Ward, Thomas +3 more
core
Sums of Products of the Terms of the Generalized Lucas Sequence {vkn}
, 2011 In this study we consider the generalized Lucas sequence {Vn} with indices in arithmetic progression. We also compute the sums of products of the terms of the Lucas sequence {Vkn} for positive odd integers ...
Kılıç, Emrah +2 more
core
Lucas Numbers and Determinants
, 2012 .In this article, we present two infinite dimensional matrices whose entries are recursively defined, and show that the sequence of their principal minors form the Lucas sequence, that ...
Hadiseh Tajbakhsh, Alireza Moghaddamfar
core +1 more source
From Lucas Sequences to Lucas Groups
, 2018 Lucas sequences, which generalize the famous Fibonacci sequence, have been studied extensively in the context of number theory and cryptography. Lucas groups, a more recently defined structure, are less studied.
Hansen, Kayson
core
Primes in shifted sums of Lucas sequences
Integers, 2017 See the abstract in the attached pdf.
Lenny Jones, Lawrence Somer
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A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences
, 2017 This paper deals with a Brocard-Ramanujan-type equation of the form un1un2 ⋯ unk+1=um2 in unknown nonnegative integers k,n1,n2, …,nk and m with k≥ 1, where u=(un)n=0∞ is either a Lucas sequence or its associated sequence.
Istvan Pink +3 more
core +1 more source
A Digital Image Confidentiality Scheme Based on Pseudo-Quantum Chaos and Lucas Sequence. [PDF]
Entropy (Basel), 2020 Butt KK, Li G, Masood F, Khan S.
europepmc +1 more source