摘要
将2级Fibonacci数与2级Lucas数的定义推广到3级,利用3级Fibonacci数与3级Lucas数之间的关系,借助几何级数的和函数以及根与系数的关系,基于3级Fibonacci数的生成函数,研究包含3级Fibonacci数的恒等变换,给出3级Fibonacci数乘积和的具体表达式,得出一些有趣的恒等式与同余式。结论推广了2级Fibonacci数列的相关结论。
The definitions of 2-order Fibonacci numbers and 2-order Lucas numbers are extended to those of order 3.By using the relation between 3-order Fibonacci numbers and 3-order Lucas numbers,the relation between roots and coefficients,and sum functions of geometric series,the identity transformations involving 3-order Fibonacci numbers are studied based on generation functions of 3-order Fibonacci numbers.The concrete expressions of the product sums of 3-order Fibonacci numbers are presented,and some interesting identities and congruences are obtained.It enriches and promotes the related conclusions of 2-order Fibonacci sequences.
作者
杨衍婷
YANG Yanting(School of Mathematics and Statistics,Xianyang Normal University,Xianyang 712000,Shaanxi,China)
出处
《咸阳师范学院学报》
2022年第2期1-4,共4页
Journal of Xianyang Normal University
基金
咸阳师范学院青年骨干教师计划项目(XSYGG201801)。
