Results 21 to 30 of about 9,638,460 (174)
On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]
Mathematica BohemicaWe consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis +3 more
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On generalized Pell numbers and their graph representations [PDF]
, 2008 In this paper we give a generalization of the Pell numbers and the Pell-Lucas numbers and next we apply this concept for their graph representations. We shall show that the generalized Pell numbers and the Pell-Lucas numbers are equal to the total number
Włoch, Iwona
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Pseudoprimality related to the generalized Lucas sequences [PDF]
, 2021 Some arithmetic properties and new pseudoprimality results concerning generalized Lucas sequences are presented. The findings are connected to the classical Fibonacci, Lucas, Pell, and Pell–Lucas pseudoprimality.
Andrica, Dorin, Bagdasar, Ovidiu
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Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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Binomial Transform of the Generalized Third Order Pell Sequence
, 2021 In this paper, we define the binomial transform of the generalized third order Pell sequence and as special cases, the binomial transform of the third order Pell, third Order Pell-Lucas and modified third order Pell sequences will be introduced.
Yüksel Soykan
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Binomial Transform of the Generalized Fourth Order Pell Sequence
, 2021 In this study, we define the binomial transform of the generalized fourth order Pell sequenceand as special cases, the binomial transform of the fourth order Pell and fourth order Pell-Lucassequences will be introduced. We investigate their properties in
Yüksel Soykan
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Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials
Discrete Dynamics in Nature and Society, 2012 We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci +2 more
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Generalized Pell numbers, balancing numbers and binary quadratic forms [PDF]
Creative Mathematics and Informatics, 2014 In this work, we derive some algebraic identities on generalized Pell numbers and their relationship with balancing numbers. Also we deduce some results on binary quadratic forms involving Pell and balancing numbers.
TEKCAN, AHMET, MERVE, TAYAT
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On the sum of the reciprocals of $$\pmb {k}$$-generalized Pell numbers
Indian Journal of Pure and Applied Mathematics, 2023 Let \( \{P_{n}^{(k)}\}_{n\ge -(k-2)} \) be the \( k \)-generalized Pell sequence given by \begin{align*} P_n^{(k)}=2P_{n-1}^{(k)}+\cdots +P_{n-k}^{(k)}\quad \text{for all }\quad n\ge 2, \end{align*} with the initial conditions \begin{align*} P_{-(n-2)}^{(k)}=P_{-(n-3)}^{(k)}=\cdots =P_{0}^{(k)}=0 \quad \text{and} \quad P_{1}^{(k)}=1. \end{align*} When \
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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
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