Results 21 to 30 of about 375 (151)

On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]

Mathematica Bohemica
We 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, Gersica Freitas, Alessandra Kreutz, Elaine Silva   +3 more
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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
doaj   +1 more source

Non-Fisherian generalized Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Using 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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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 $k$-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
doaj   +1 more source

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, Mirac Cetin Firengiz, Naim Tuglu   +2 more
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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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A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients

Communications in Advanced Mathematical Sciences
In this study, we define a new generalization of the hybrid $k$-Pell sequence consisting of hybrid numbers with generalized hybrid $k$-Pell numbers as coefficients.
Elen Viviani Pereira Spreafico, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino   +2 more
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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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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)
openaire   +1 more source