A378477 The number of n-colorings of the vertices of the truncated icosidodecahedron up to rotation and reflection.

0, 1, 11076899964874299238703297447907328, 14975085832620260086776498590197757887552760437584786915, 14723725539819869413194145839524321308612931385268246121155792029614080, 6269303204385533375833261531851976948366440371233447120478861810030555725146484375

Offset: 0

Author

Peter Kagey, Nov 27 2024

Keywords

• nonn

Comments

Equivalently, the number of n-colorings of the faces of the disdyakis triacontahedron, which is the polyhedral dual of the truncated octahedron.

Colorings are counted up to the full icosahedral symmetry group of order 120.

Links

• Wikipedia, Disdyakis triacontahedron
• Wikipedia, Truncated icosidodecahedron

Crossrefs

Cf. A000332, A060530, A128766, A199406, A252704, A252705, A274900, A337963, A378473, A378474, A378475, A378476, A378478.

Formula

a(n) = 1/120*(n^120 + 31*n^60 + 20*n^40 + 24*n^24 + 20*n^20 + 24*n^12).

Asymptotically, a(n) ~ n^120/120