何天晓.递推数列的非线性表达式的构造[J].数学研究及应用,2015,35(5):473~483
递推数列的非线性表达式的构造
Construction of Nonlinear Expression for Recursive Number Sequences
投稿时间:2015-04-28  最后修改时间:2015-07-08
DOI:10.3770/j.issn:2095-2651.2015.05.001
中文关键词:  Fibonacci 数  Pell 数  Jacobsthal数  Lucas数  线性递推关系  脉冲响应序列
英文关键词:Fibonacci numbers  Pell numbers  Jacobsthal numbers  Lucas numbers  linear recurrence relation  Horadam sequence  impulse response sequence
基金项目:
作者单位
何天晓 伊利诺伊卫斯理大学数学系, 布鲁明顿 伊利诺伊 61702-2900 
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中文摘要:
      受徐文[9]的启发,本文建立一类Lucas数列的非线性表达式.作者还应用该数列与其它2阶线性递推数列的关系,将上述表达式推广到众多2阶递推数列.
英文摘要:
      A type of nonlinear expressions of Lucas sequences are established inspired by Hsu [A nonlinear expression for Fibonacci numbers and its consequences. J. Math. Res. Appl., 2012, 32(6): 654--658]. Using the relationships between the Lucas sequence and other linear recurring sequences satisfying the same recurrence relation of order $2$, i.e., the Horadam sequences, we may transfer the identities of Lucas sequences to the latter.
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