n-color1-2-3 compositions of positive integers

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.