%N Number of regular-faced convex polyhedra (excluding prisms and antiprisms) with exactly n types of faces.
%C The regular-faced convex polyhedra other than prisms and antiprisms are the Platonic, Archimedean, and Johnson solids.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_Johnson_solids">List of Johnson solids</a>
%F a(n) = 0 for n >= 5.
%e Each of the five Platonic solids, and each of five Johnson solids, has one type of face, so a(1) = 5 + 5 = 10.
%e Each of ten Archimedean solids, and each of thirty-five Johnson solids, has two types of faces, so a(2) = 10 + 35 = 45.
%e Each of three Archimedean solids, and each of thirty-five Johnson solids, has three types of faces, so a(3) = 3 + 35 = 38.
%e Each of seventeen Johnson solids has four types of faces, so a(4) = 17.
%Y Cf. A299114, A299529.
%A _Jonathan Sondow_, Feb 11 2018