Results 11 to 20 of about 9,638,460 (174)
Generalized sum of Pell Numbers [PDF]
, 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).
Sparavigna, Amelia Carolina +1 more
openaire +3 more sources
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.
Yüksel Soykan, Soykan, Yüksel
openaire +4 more sources
On a new class of the generalized Gauss k-Pell numbers and their polynomials
Notes on Number Theory and Discrete Mathematics, 2022 In this article, we generalize the well-known Gauss Pell numbers and refer to them as generalized Gauss k-Pell numbers. There are relationships discovered between the class of generalized Gauss k-Pell numbers and the typical Gauss Pell numbers. Also, we generalize the known Gauss Pell polynomials, and call such polynomials as the generalized Gauss k ...
Kaya, Ahmet, Özimamoğlu, Hayrullah
openaire +3 more sources
On Generalized Third-Order Pell Numbers
Asian Journal of Advanced Research and Reports, 2019 In this paper, we investigate the generalized third order Pell sequences and we deal with, in detail, three special cases which we call them third order Pell, third order Pell-Lucas and modified third order Pell sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
Yüksel Soykan, Soykan, Yüksel
openaire +5 more sources
Properties of Generalized Fifth-Order Pell Numbers
Asian Research Journal of Mathematics, 2019 In this paper, we investigate the generalized fifth order Pell sequences and we deal with, in detail, three special cases which we call them as fifth order Pell, fifth order Pell-Lucas and modied fifth order Pell sequences.
Yüksel Soykan
openaire +4 more sources
THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-$k$ PELL NUMBERS
Taiwanese Journal of Mathematics, 2006 In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the
Kiliç, Emrah, Taşci, Dursun
openaire +5 more sources
, 2023 In this paper, generalized Pell graphs $Pi_{n,k}$, $kge 2$, are introduced. The special case of $k=2$ are the Pell graphs $Pi_{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established.
Tan, Elif +2 more
core +4 more sources
Pell-Padovan generalized quaternions [PDF]
, 2021 The aim of this article is to introduce Pell-Padovan generalized quaternions. It also derives new properties associated with these and takes into account negative indices. Additionally, it presents generating function, Binet-like formula, Simson formula,
Isbilir, Zehra +3 more
core +1 more source
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 GENERALIZED SIXTH-ORDER PELL SEQENCES [PDF]
, 2020 In this paper, we investigate the generalized sixth order Pell sequences and we deal with, in detail, three special cases which we call them as sixth order Pell, sixth order Pell-Lucas and modified sixth order Pell ...
Yüksel SOYKAN, SOYKAN, Yüksel
core +1 more source