We derive the generating function (g.f.) of the number of colored circular palindromic compositions of with parts in terms of the g.f. of an input sequence that determines how many different colors each part of the composition can have. As a result, we get the g.f. of the number of all colored circular palindromic compositions of . Using the latter formula and the g.f. of the number of colored circular compositions, we may easily derive the g.f. of the number of all colored dihedral compositions of .
"Generalized colored circular palindromic compositions." Mosc. J. Comb. Number Theory 9 (2) 173 - 186, 2020. https://doi.org/10.2140/moscow.2020.9.173