关于双倍和四倍斐波那契类型序列

Annales Mathematicae Silesianae Pub Date : 2023-11-22 DOI:10.2478/amsil-2023-0020

Nur Şeyma Yilmaz, A. Włoch, Engin Özkan, Dominik Strzałka

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引用次数: 0

摘要

摘要本文研究了通过对斐波那契数列进行距离广义化而得到的双倍和四倍斐波那契数列族。我们特别得到了双倍斐波那契序列、双倍和四倍帕多万序列以及四倍纳拉亚纳序列。我们用图形方法给出了这些序列的二项式直接公式，还推导出了一些同式。此外，我们还研究了这些序列的矩阵生成器，并确定了它们与帕斯卡三角形的联系。

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On Doubled and Quadrupled Fibonacci Type Sequences

Abstract In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle.

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Annales Mathematicae Silesianae

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