Results 21 to 30 of about 1,421 (176)
Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence
Aksaray University Journal of Science and Engineering, 2018 In this paper, we first define the Gaussian modified Pell sequence, for n ≥ 2, by the relation = 2 + with initial conditions = 1 ─ i and = 1 + i. Then we give the definition of the Gaussian modified Pell polynomial sequence, for n ≥ 2, by the relation = 2 + with initial conditions = 1─ xi and = x + i.
YAGMUR, Tulay, KARAASLAN, Nusret
openaire +4 more sources
On the Characteristic Polynomial of the Generalized k-Distance Tribonacci Sequences
Mathematics, 2020 In 2008, I. Włoch introduced a new generalization of Pell numbers. She used special initial conditions so that this sequence describes the total number of special families of subsets of the set of n integers.
Pavel Trojovský
doaj +1 more source
On New Polynomial Sequences Constructed to Each Vertex in an n-Gon
Discrete Dynamics in Nature and Society, 2022 In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n-gon. We compute the relation among the polynomials with such vertices.
Abdul Hamid Ganie +3 more
doaj +1 more source
On Pillai’s problem with the Fibonacci and Pell sequences [PDF]
Boletín de la Sociedad Matemática Mexicana, 2018 Let \( (F_n)_{n\ge 0} \) and \( (P_n)_{n\ge 0} \) be the sequences of Fibonacci and Pell numbers given by \( F_0=P_0=0, ~ F_1 = P_1=1 \), \( F_{n+2}=F_{n+1}+F_n \), and \( P_{n+2}=2P_{n+1}+P_n \) for all \( n\ge 0 \), respectively. In the paper under review, the authors study the Pillai type problem: \begin{align*} F_n-P_m = F_{n_1}-P_{m_1} = c\tag{1} \
Santos Hernández Hernández +2 more
openaire +2 more sources
Lucas sequences and repdigits [PDF]
Mathematica Bohemica, 2022 Let $(G_n)_{n \geq1}$ be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are $\{U_n\}$ and $\{V_n\}$, respectively.
Hayder Raheem Hashim, Szabolcs Tengely
doaj +1 more source
Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
doaj +1 more source
Floor and ceiling functions for Pell numbers [PDF]
Notes on Number Theory and Discrete MathematicsThe analytical study of the Pell number and the role of floor and ceiling functions into their computation is examined. Closed expressions of Pell numbers were initially derived using Binet's formula, followed by an asymptotic behavior study of the ...
İsmail Sulan, Mustafa Aşçı
doaj +1 more source
Bi-Periodic Pell Sequence [PDF]
Academic Journal of Applied Mathematical Sciences, 2020 In this study, we introduce a new generalization of the Pell numbers which is called bi-periodic Pell sequences. We then proceed to find the Binet formula as well as the generating function for this sequence. The well-known Cassini, Catalan and the D’ocagne’s identities as well as some related binomial summation and sum formulas are also given.
S. Uygun, H. Karataş
openaire +1 more source
The Properties of Binomial Transforms for Modified (s,t)-Pell Matrix Sequence
Communications in Advanced Mathematical SciencesIn this study, we investigate a generalization of the modified Pell sequence, which is called $(s,t)$-modified Pell sequence. By considering this sequence, we define the matrix sequence whose elements are $(s,t)$-modified Pell numbers.
Ozan Haklıdır, Şükran Uygun
doaj +1 more source
On Hyper k-Pell, Hyper k-Pell-Lucas and Hyper Modified k-Pell Sequences
, 2022 See the abstract in the attached pdf.
Catarino, Paula +2 more
openaire +3 more sources