以Fibonacci和Lucas数为权的二项式恒等式

Some binomial identities with Fibonacci and Lucasnumbers as weights

得到了一些以Fibonacci数和Lucas数为权的二项式和。首先给出了最近由Robert在期刊Fibonacci Quarterly上提出的H-882问题的解,其次给出了有限二项式和n∑k=0(n+k n-k)Q_(k)的显示表达式及n∑k=0(n+k k)Q_(k)的另一种用中心二项式系数表达的有趣形式,这里Q_(k)代表Fibonacci数F_(k)或者Lucas数L_(k)。

Some binomial sums with Fibonacci and Lucas numbers as weights are established.Among others,a solution to the problem H-882 proposed recently by Robert is first given.And then the explicit formula for the finite binomial sum n∑k=0(n+k n-k)Q_(k)is derived.In addition,another interesting expression concerning central binomial coefficient for the sum n∑k=0(n+k k)Q_(k)is obtained,where the Q_(k) stands for Fibonacci number F_(k) or Lucas number L_(k).