Results 11 to 20 of about 623 (119)
Summing a Family of Generalized Pell Numbers [PDF]
Annales Mathematicae Silesianae, 2020 Abstract A new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power
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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
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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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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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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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Generalized sum of Pell Numbers
, 2021 Here we are proposing a generalized sum for Pell numbers. This sum contains four Pell numbers. By means of this generalized sum, the Pell number at position (n+m) in the sequence is given by the Pell numbers at positions n, m, (n-1) and (m-1).
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Generalized Pell-Padovan Numbers
Asian Journal of Advanced Research and Reports, 2020 In this paper, we investigate the generalized Pell-Padovan sequences and we deal with, in detail, four special cases, namely, Pell-Padovan, Pell-Perrin, third order Fibonacci-Pell and third order Lucas-Pell sequences. We present Binet’s formulas, generating functions, Simson formulas and the summation formulas for these sequences.
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On a New One Parameter Generalization of Pell Numbers [PDF]
Annales Mathematicae Silesianae, 2019 Abstract In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r -Pell numbers. Moreover, we give a graph interpretation of these numbers.
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Convolutions of the generalized Pell and Pell-Lucas numbers
Filomat, 2016 We consider the convolution of the generalized Pell numbers-P(s) n,m and the convolution of the generalized Pell-Lucas numbers-Q(s) n,m. For s = 0, the sequence P(0) n,m represents the generalized Pell numbers Pn;m, and the sequence Q(0) n,m represents the generalized Pell-Lucas numbers Qn,m ([1], [2]). For m = 2 and s = 0, the numbers P(0)
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