Results 21 to 30 of about 9,774,386 (178)
p-Analogue of biperiodic Pell and Pell–Lucas polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, a binomial sum, unlike but analogous to the usual binomial sums, is expressed with a different definition and termed the p-integer sum. Based on this definition, p-analogue Pell and Pell–Lucas polynomials are established and the generating
Bahar Kuloğlu +2 more
doaj +1 more source
On Sums of Squares of Pell-Lucas Numbers
Integers, 2006 In this paper we prove several formulas for sums of squares of even Pell-Lucas numbers, sums of squares of odd Pell-Lucas numbers, and sums of products of even and odd PellLucas numbers. These sums have nice representations as products of appropriate Pell and Pell-Lucas numbers with terms from certain integer sequences.
Cerin Z., GIANELLA, Gian Mario
openaire +5 more sources
A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
doaj +1 more source
On Generalized Pell and Pell–Lucas Numbers [PDF]
Iranian Journal of Science and Technology, Transactions A: Science, 2019 In this paper, we introduce and study a new one-parameter generalization of Pell numbers. We describe their distinct properties also related to matrix representation.
Lucyna Trojnar-Spelina, Iwona Włoch
openaire +1 more source
Fibonacci–Lucas–Pell–Jacobsthal relations [PDF]
, 2022 In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant ...
Goy, Taras +5 more
core +3 more sources
On some new arithmetic properties of the generalized Lucas sequences [PDF]
, 2021 Some arithmetic properties of the generalized Lucas sequences are studied, extending a number of recent results obtained for Fibonacci, Lucas, Pell, and Pell–Lucas sequences.
Andrica, Dorin, Bagdasar, Ovidiu
core +1 more source
On Pell and Pell-Lucas Generalized Octonions
, 2021 In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra O(a, b, c) where a, b and c are real numbers. For these number sequences, we obtain Binet formulas and gave some wellknown identities such as Catalan’s identity ...
Ümit TOKEŞER, Tuğba MERT, Göksal Bilgici, Zafer ÜNAL
core +2 more sources
On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
doaj +1 more source
A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence)
Communications in Mathematics and Applications, 2019 In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as \begin{align*} Q_{n}= \begin{cases} 2bQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is even} \\ 2aQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is odd}% \end{cases} \text{\ \ }n\geq 2, \end{align*} with ...
Sukran Uygun, Hasan Karatas
openaire +2 more sources
Abstract and Applied Analysis, 2014 Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial.
Tingting Xu, Zhaolin Jiang, Ziwu Jiang
doaj +1 more source