The k-nacci triangle and applications
A generalization of the classical Fibonacci numbers $ F_n $ is the k-generalized Fibonacci numbers $ F_n^{(k)} $ for $ n \ge 2-k $ whose first k terms are $ 0, \, \ldots ,\, 0,\, 1 $ and each term afterward is the sum of the preceding k terms. In this article, we first introduce the k-nacci triangle...
Ausführliche Beschreibung
Autor*in: |
Kantaphon Kuhapatanakul [verfasserIn] Pornpawee Anantakitpaisal [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
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2017 |
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In: Cogent Mathematics - Taylor & Francis Group, 2015, 4(2017), 1 |
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Übergeordnetes Werk: |
volume:4 ; year:2017 ; number:1 |
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DOI / URN: |
10.1080/23311835.2017.1333293 |
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Katalog-ID: |
DOAJ037839411 |
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10.1080/23311835.2017.1333293 doi (DE-627)DOAJ037839411 (DE-599)DOAJ3d36920ecb9f4a918e18e93acb127f6f DE-627 ger DE-627 rakwb eng QA1-939 Kantaphon Kuhapatanakul verfasserin aut The k-nacci triangle and applications 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A generalization of the classical Fibonacci numbers $ F_n $ is the k-generalized Fibonacci numbers $ F_n^{(k)} $ for $ n \ge 2-k $ whose first k terms are $ 0, \, \ldots ,\, 0,\, 1 $ and each term afterward is the sum of the preceding k terms. In this article, we first introduce the k-nacci triangle to derive an explicit formula of the nth k-generalized Fibonacci number. Second, we also introduce the k-generalized Pascal triangle for deriving the formula of the k-generalized Fibonacci numbers. k-generalized Fibonacci numbers Fibonacci numbers Pascal triangle k-nacci triangle binomial coefficient Mathematics Pornpawee Anantakitpaisal verfasserin aut In Cogent Mathematics Taylor & Francis Group, 2015 4(2017), 1 (DE-627)823090817 (DE-600)2818161-X 23311835 nnns volume:4 year:2017 number:1 https://doi.org/10.1080/23311835.2017.1333293 kostenfrei https://doaj.org/article/3d36920ecb9f4a918e18e93acb127f6f kostenfrei http://dx.doi.org/10.1080/23311835.2017.1333293 kostenfrei https://doaj.org/toc/2331-1835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2017 1 |
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10.1080/23311835.2017.1333293 doi (DE-627)DOAJ037839411 (DE-599)DOAJ3d36920ecb9f4a918e18e93acb127f6f DE-627 ger DE-627 rakwb eng QA1-939 Kantaphon Kuhapatanakul verfasserin aut The k-nacci triangle and applications 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A generalization of the classical Fibonacci numbers $ F_n $ is the k-generalized Fibonacci numbers $ F_n^{(k)} $ for $ n \ge 2-k $ whose first k terms are $ 0, \, \ldots ,\, 0,\, 1 $ and each term afterward is the sum of the preceding k terms. In this article, we first introduce the k-nacci triangle to derive an explicit formula of the nth k-generalized Fibonacci number. Second, we also introduce the k-generalized Pascal triangle for deriving the formula of the k-generalized Fibonacci numbers. k-generalized Fibonacci numbers Fibonacci numbers Pascal triangle k-nacci triangle binomial coefficient Mathematics Pornpawee Anantakitpaisal verfasserin aut In Cogent Mathematics Taylor & Francis Group, 2015 4(2017), 1 (DE-627)823090817 (DE-600)2818161-X 23311835 nnns volume:4 year:2017 number:1 https://doi.org/10.1080/23311835.2017.1333293 kostenfrei https://doaj.org/article/3d36920ecb9f4a918e18e93acb127f6f kostenfrei http://dx.doi.org/10.1080/23311835.2017.1333293 kostenfrei https://doaj.org/toc/2331-1835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2017 1 |
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A generalization of the classical Fibonacci numbers $ F_n $ is the k-generalized Fibonacci numbers $ F_n^{(k)} $ for $ n \ge 2-k $ whose first k terms are $ 0, \, \ldots ,\, 0,\, 1 $ and each term afterward is the sum of the preceding k terms. In this article, we first introduce the k-nacci triangle to derive an explicit formula of the nth k-generalized Fibonacci number. Second, we also introduce the k-generalized Pascal triangle for deriving the formula of the k-generalized Fibonacci numbers. |
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A generalization of the classical Fibonacci numbers $ F_n $ is the k-generalized Fibonacci numbers $ F_n^{(k)} $ for $ n \ge 2-k $ whose first k terms are $ 0, \, \ldots ,\, 0,\, 1 $ and each term afterward is the sum of the preceding k terms. In this article, we first introduce the k-nacci triangle to derive an explicit formula of the nth k-generalized Fibonacci number. Second, we also introduce the k-generalized Pascal triangle for deriving the formula of the k-generalized Fibonacci numbers. |
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A generalization of the classical Fibonacci numbers $ F_n $ is the k-generalized Fibonacci numbers $ F_n^{(k)} $ for $ n \ge 2-k $ whose first k terms are $ 0, \, \ldots ,\, 0,\, 1 $ and each term afterward is the sum of the preceding k terms. In this article, we first introduce the k-nacci triangle to derive an explicit formula of the nth k-generalized Fibonacci number. Second, we also introduce the k-generalized Pascal triangle for deriving the formula of the k-generalized Fibonacci numbers. |
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score |
7.400772 |