二项式系数与Lucas数4q次幂的关系

Relation between binomial coefficients and 4q-power of Lucas numbers

结合Lucas数列与二项式系数的定义及性质,利用初等数论的方法研究了二项式系数与Lucas数的4q次幂的卷积并给出了证明,得到了二项式系数与Lucas数4q次幂之间的恒等式关系,推广了已有的组合数与Lucas数的较小正整数次幂的恒等式相关结果.

According to the definition and the properties of the Lucas sequence and combinatorial numbers, the identity relationship between the binomial coefficient and 4q-powers of the Lucas numbers is proved by using methods of elementary number theory, thus generalizing the related results of identity of the lower positive integer power of combinatorial number and Lucas number.