Common terms of k-Pell numbers and Padovan or Perrin numbers
Abstract Let $$k\ge 2$$ k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are $$0,\ldots ,0,1$$ 0 , … , 0 , 1 and each term afterwards is given by the linear recurrence $$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Arabian Journal of Mathematics |
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| Online Access: | https://doi.org/10.1007/s40065-022-00407-8 |
| _version_ | 1797865518563065856 |
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| author | Benedict Vasco Normenyo Salah Eddine Rihane Alain Togbé |
| author_facet | Benedict Vasco Normenyo Salah Eddine Rihane Alain Togbé |
| author_sort | Benedict Vasco Normenyo |
| collection | DOAJ |
| description | Abstract Let $$k\ge 2$$ k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are $$0,\ldots ,0,1$$ 0 , … , 0 , 1 and each term afterwards is given by the linear recurrence $$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}. \end{aligned}$$ P n ( k ) = 2 P n - 1 ( k ) + P n - 2 ( k ) + ⋯ + P n - k ( k ) . In this paper, we extend the previous work (Rihane and Togbé in Ann Math Inform 54:57–71, 2021) and investigate the Padovan and Perrin numbers in the k-Pell sequence. |
| first_indexed | 2024-04-09T23:09:21Z |
| format | Article |
| id | doaj.art-0e54a05f03dd40969846dd8fa972e8d4 |
| institution | Directory Open Access Journal |
| issn | 2193-5343 2193-5351 |
| language | English |
| last_indexed | 2024-04-09T23:09:21Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Arabian Journal of Mathematics |
| spelling | doaj.art-0e54a05f03dd40969846dd8fa972e8d42023-03-22T10:27:07ZengSpringerOpenArabian Journal of Mathematics2193-53432193-53512022-11-0112121923210.1007/s40065-022-00407-8Common terms of k-Pell numbers and Padovan or Perrin numbersBenedict Vasco Normenyo0Salah Eddine Rihane1Alain Togbé2Department of Mathematics, University of GhanaDepartment of Mathematics, Institute of Science and Technology, University Center of MilaDepartment of Mathematics and Statistics, Purdue University NorthwestAbstract Let $$k\ge 2$$ k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are $$0,\ldots ,0,1$$ 0 , … , 0 , 1 and each term afterwards is given by the linear recurrence $$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}. \end{aligned}$$ P n ( k ) = 2 P n - 1 ( k ) + P n - 2 ( k ) + ⋯ + P n - k ( k ) . In this paper, we extend the previous work (Rihane and Togbé in Ann Math Inform 54:57–71, 2021) and investigate the Padovan and Perrin numbers in the k-Pell sequence.https://doi.org/10.1007/s40065-022-00407-811B3911J86 |
| spellingShingle | Benedict Vasco Normenyo Salah Eddine Rihane Alain Togbé Common terms of k-Pell numbers and Padovan or Perrin numbers Arabian Journal of Mathematics 11B39 11J86 |
| title | Common terms of k-Pell numbers and Padovan or Perrin numbers |
| title_full | Common terms of k-Pell numbers and Padovan or Perrin numbers |
| title_fullStr | Common terms of k-Pell numbers and Padovan or Perrin numbers |
| title_full_unstemmed | Common terms of k-Pell numbers and Padovan or Perrin numbers |
| title_short | Common terms of k-Pell numbers and Padovan or Perrin numbers |
| title_sort | common terms of k pell numbers and padovan or perrin numbers |
| topic | 11B39 11J86 |
| url | https://doi.org/10.1007/s40065-022-00407-8 |
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