邓玉平,谭宇.Fibonacci数列推广[J].,2011,(1):154-156 |
Fibonacci数列推广 |
Generalization of Fibonacci sequence |
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DOI:10.7511/dllgxb201101028 |
中文关键词: Fibonacci数列 推广 通项公式 特征方程 |
英文关键词: Fibonacci sequence generalization general term formula characteristic function |
基金项目:国家自然科学基金资助项目(10801022) |
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中文摘要: |
Fibonacci数列是从兔子繁殖问题引出的经典数列,从兔子繁殖角度出发,将经典 Fibonacci数列进行多种形式的推广, 总结出一般形式.利用 k 维空间上的变换方法,将代数学与几何学相结合,求出广义 k 阶Fibonacci数列的通项公式.结果表明,该通项公式可用数列的特征方程的解来表示. |
英文摘要: |
Fibonacci sequence is a classical sequence generated from the question of the rabbits′ propagation. From the viewpoint of the rabbits′ propagation, the classical Fibonacci sequence is generalized in many forms and some general forms are obtained. Combining interrelated knowledge of algebra and geometry by the transformation on k -dimensional space, the formula of general term for the generalized k -step Fibonacci sequence is obtained. The results show that the general term formula can be expressed by the solutions of the characteristic equation of the sequence. |
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