<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we define the Pell-Pell <italic>p</italic>-sequence and then we discuss the connection of the Pell-Pell <italic>p</italic>-sequence with Pell and Pell <italic>p</italic>-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Pell-Pell <italic>p</italic>-numbers by the aid of the <italic>n</italic>th power of the generating matrix the Pell-Pell <italic>p</italic>-sequence. Furthermore, we obtain an exponential representation of the Pell-Pell p-numbers and we develop relationships between the Pell-Pell <italic>p</italic>-numbers and their permanent, determinant and sums of certain matrices.</p></abstract>

In this paper, we define the Pell-Pell p-sequence and then we discuss the connection of the Pell-Pell p-sequence with Pell and Pell p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Pell-Pell p-numbers by the aid of the nth power of the generating matrix the Pell-Pell p-sequence. Furthermore, we obtain an exponential representation of the Pell-Pell p-numbers and we develop relationships between the Pell-Pell p-numbers and their permanent, determinant and sums of certain matrices.

Matrix Manipulations for Properties of Pell <italic>p</italic>-Numbers and their Generalizations

Department of Mathematics, Faculty of Science and Letters

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Matrix Manipulations for Properties of Pell -Numbers and their Generalizations

In this paper, we define the Pell-Pell p-sequence and then we discuss the connection of the Pell-Pell p-sequence with Pell and Pell p-sequences. Also, we...

Matrix Manipulations for Properties of Pell p-Numbers and their Generalizations

Published Online: Dec 28, 2020

Page range: 89 - 102

Received: Oct 31, 2019

Accepted: Jan 09, 2020

DOI: https://doi.org/10.2478/auom-2020-0036

Keywords
Pell sequence, Pell p-sequence, Matrix, Representation

© 2020 Özgür Erdağ et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Matrix Manipulations for Properties of Pell p-Numbers and their Generalizations

Published Online: Dec 28, 2020

Page range: 89 - 102

Received: Oct 31, 2019

Accepted: Jan 09, 2020

DOI: https://doi.org/10.2478/auom-2020-0036

KeywordsPell sequence, Pell p-sequence, Matrix, Representation

© 2020 Özgür Erdağ et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Pell sequence, Pell p-sequence, Matrix, Representation