2个特殊的二次线性递推序列

TWO QUADRATIC LINEAR RECURRENCES

研究了线性递推序列an=an-1+kbn-1,bn=an-1+bn-1和An=6An-1-An-2。通过不同的计算方法,得到了相关组合恒等式。给出了Fibonacci数、Lucas数的新的显示表达式。

Two quadratic linear recurrent systems, a_n = a_(n-1) + kb_(n-1),b_n = a_(n-1) + b_(n-1) and A_n = 6 A_(n-1 )– A_(n-2) are investigated. Some results related to Fibonacci number are obtained, and combinatorial identities are derived by different computing methods.