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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data:Tiling and combinatorial interpretations of these numbers are presented, and explicit formulas that allow us to calculate the nth number are given.
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Conclusion & Impact: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.
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.
TAŞYURDU, Y., CENGİZ, B. (2023). On Fibonacci (k,p)-Numbers and Their Interpretations. Sakarya University Journal of Science, Cilt: 27 Sayı: 2, 235–246. https://ajindex.com/articles/941655
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