Results 31 to 40 of about 1,668,226 (212)

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
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Floor and ceiling functions for Pell numbers [PDF]

Notes on Number Theory and Discrete Mathematics
The 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

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
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Some algebraic identities on quadra Fibona-Pell integer sequence [PDF]

, 2015
WOS: 000354627000002In this work, we define a quadra Fibona-Pell integer sequence W-n = 3W(n-1) - 3W(n-3) - Wn-4 for n >= 4 with initial values W-0 = W-1 = 0, W-2 = 1, W-3 = 3, and we derive some algebraic identities on it including its relationship with
Arzu Özkoç, Özkoç, Arzu
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De Moivre-Type Identities for the Pell Numbers [PDF]

, 2021
This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers.Moreover, we obtain the De Moivre-type identities for these numbers.
Mücahit AKBIYIK, Seda YAMAÇ AKBIYIK, Akbıyık, Mücahit, Akbıyık, Seda Yamaç   +3 more
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FAREY-PELL SEQUENCE, APPROXIMATION TO IRRATIONALS AND HURWITZ'S INEQUALITY [PDF]

, 2016
The purpose of this paper is to give the notion of Farey-Pell sequence. We investigate some identities of the Farey-Pell sequence. Finally, a generalization of Farey-Pell sequence and an approximation to irrationals via Farey-Pell fractions are ...
Kizilaslan, Gonca, Akkus, Ilker, Irmak, Nurettin   +2 more
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On Hyper k-Pell, Hyper k-Pell-Lucas and Hyper Modified k-Pell Sequences

, 2022
See the abstract in the attached pdf.
Catarino, Paula, Alves, Francisco R. V., Campos, Helena   +2 more
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A new quadra polynomial sequence [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define a new quadra polynomial sequence by using Özkoç numbers as the coefficients. Then, we derive some properties for this polynomial sequence by the help of Fibonacci and Pell polynomials.
Emre Sevgi
doaj   +1 more source

On $k$-Pell numbers which are sum of two Narayana's cows numbers [PDF]

Mathematica Bohemica
For any positive integer $k\geq2$, let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence which starts with $0,\cdots,0,1$ ($k$ terms) with the linear recurrence P_n^{(k)} = 2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\quad\text{for} n\
Kouèssi Norbert Adédji, Mohamadou Bachabi, Alain Togbé   +2 more
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Pell and Pell–Lucas Sequences of Fractional Order

Fractal and Fractional
The purpose of this paper is to introduce the fractional Pell numbers, together with several properties, via a Grünwald–Letnikov fractional operator of orders q∈(0,1) and q∈(1,2). This paper also explores the fractional Pell–Lucas numbers and their properties.Due to the long-term memory property, fractional Pell sequences and fractional Pell–Lucas ...
Jagan Mohan Jonnalagadda, Marius-F. Danca   +1 more
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