A378478 The number of n-colorings of the vertices of the snub dodecahedron up to rotation.

0, 1, 19215358678900736, 706519304586988199183738259, 22153799929748598169960860333637632, 14456028966473392453665534687042333984375, 814561299678154291488767806377392301451223040, 8467031012327056088703142262372040966699399765293

Offset: 0

Author

Peter Kagey, Nov 27 2024

Keywords

• nonn

Comments

Equivalently, the number of n-colorings of the faces of the pentagonal hexecontahedron, which is the polyhedral dual of the snub dodecahedron.

Colorings are counted up to the rotational icosahedral symmetry group of order 60.

Links

• Wikipedia, Pentagonal hexecontahedron
• Wikipedia, Snub dodecahedron

Crossrefs

Cf. A000332, A060530, A128766, A199406, A252704, A252705, A274900, A337963, A378473, A378474, A378475, A378476, A378477.

Formula

a(n) = 1/60*(n^60 + 15*n^30 + 20*n^20 + 24*n^12).

Asymptotically, a(n) ~ n^60/60.