On Fibonacci (k,p)-Numbers and Their Interpretations
In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to a new parameter k. Tiling and combinatorial i...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sakarya University
2023-04-01
|
| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2641812 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846111410056069120 |
|---|---|
| author | Berke Cengiz Yasemin Taşyurdu |
| author_facet | Berke Cengiz Yasemin Taşyurdu |
| author_sort | Berke Cengiz |
| collection | DOAJ |
| description | In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to a new parameter k. Tiling and combinatorial interpretations of these numbers are presented, and explicit formulas that allow us to calculate the nth number are given. Also, their generating functions are obtained and sums formulas of these numbers with special subscripts are given by tiling interpretations that allow the derivation of their properties. |
| format | Article |
| id | doaj-art-84b7fdadb87b4e34b814b686837a85c7 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-04-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-84b7fdadb87b4e34b814b686837a85c72024-12-23T08:15:22ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-04-0127223524610.16984/saufenbilder.117317328On Fibonacci (k,p)-Numbers and Their InterpretationsBerke Cengiz0https://orcid.org/0000-0001-8372-3332Yasemin Taşyurdu1https://orcid.org/0000-0002-9011-8269ERZINCAN BINALI YILDIRIM UNIVERSITYErzincan Binali Yıldırım ÜniversitesiIn this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to a new parameter k. Tiling and combinatorial interpretations of these numbers are presented, and explicit formulas that allow us to calculate the nth number are given. Also, their generating functions are obtained and sums formulas of these numbers with special subscripts are given by tiling interpretations that allow the derivation of their properties.https://dergipark.org.tr/tr/download/article-file/2641812combinatorial identitiesfibonacci p-numbersgeneralized fibonacci numberstilings |
| spellingShingle | Berke Cengiz Yasemin Taşyurdu On Fibonacci (k,p)-Numbers and Their Interpretations Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi combinatorial identities fibonacci p-numbers generalized fibonacci numbers tilings |
| title | On Fibonacci (k,p)-Numbers and Their Interpretations |
| title_full | On Fibonacci (k,p)-Numbers and Their Interpretations |
| title_fullStr | On Fibonacci (k,p)-Numbers and Their Interpretations |
| title_full_unstemmed | On Fibonacci (k,p)-Numbers and Their Interpretations |
| title_short | On Fibonacci (k,p)-Numbers and Their Interpretations |
| title_sort | on fibonacci k p numbers and their interpretations |
| topic | combinatorial identities fibonacci p-numbers generalized fibonacci numbers tilings |
| url | https://dergipark.org.tr/tr/download/article-file/2641812 |
| work_keys_str_mv | AT berkecengiz onfibonaccikpnumbersandtheirinterpretations AT yasemintasyurdu onfibonaccikpnumbersandtheirinterpretations |