递推数列的非线性表达式的构造

Construction of Nonlinear Expression for Recursive Number Sequences

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

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.