摘要
考虑了正整数n的有序分拆中,分部量1有两种形式的情形,发现正整数n的分部量1有两种形式的有序分拆数等于第2n+1个Fiboacci数F2n+1.进一步得到了一个涉及正整数n的分部量1有两种形式的有序分拆数与正整数的n-color有序分拆数之间的一个恒等式.并且给出了正整数n的分部量1有两种形式的有序分拆数的一个显式计数公式.
In this paper, we considered the compositions with the part 1 has two kinds, and found that the number of compositions with the part 1 has two kinds equals the(2n + 1)^(th) Fibonacci number F2n+1. Furthermore, we obtained an identity between the number of compositions of n when part 1 can be of two kinds and the number of n-color compositions. And we also give an explicit counting formula of the number of compositions of n when part 1 can be of two kinds.
出处
《纯粹数学与应用数学》
2016年第5期441-447,共7页
Pure and Applied Mathematics
基金
国家自然科学基金(11461020)
