正整数n-color 1-2-3有序分拆（英文）

n-color 1-2-3 compositions of positive integers

正整数的n-color 1-2-3有序分拆是指正整数的只含分部量是1,2或者3的n-color有序分拆,而正整数的回文的n-color 1-2-3有序分拆是指只含有分部量是1,2或者3的n-color有序分拆且分部量从左往右读与从右往左读是相等的.给出了正整数的n-color 1-2-3有序分拆数和回文的n-color 1-2-3有序分拆数的生成函数、显式公式以及递推公式.还给出了正整数的1-2-3有序分拆数和正整数不含分部量是3的倍数的有序分拆数之间的一个关系式以及推广形式.

An n-color 1-2-3 composition of positive integers is defined as an n-color composition with only parts of size 1,2 or 3.An n-color 1-2-3 palindromic composition is an n-color 1-2-3 composition that reads the same forward as backward.Here the generating function,explicit formulas and recurrence relations for the number of n-color 1-2-3 compositions and the n-color 1-2-3 palindromic compositions of positive integers were obtained.In addition,a relation between the number of 1-2-3 compositions of a positive integer and the number of compositions of a positive integer with parts omitting all multiples of size 3 was given.Furthermore,the generalized relation was obtained.