A378474 The number of n-colorings of the vertices of the truncated cuboctahedron up to rotation and reflection.

0, 1, 5864068667776, 1661800897546646288751, 1650586719047285117763813376, 74014868308343792955106160546875, 467755368903219944377426648894114176, 764653504526960946768130306131125170501, 464598858302721315450530067459906444722176

Offset: 0

Author

Peter Kagey, Nov 27 2024

Keywords

• nonn
• easy

Comments

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

Colorings are counted up to the full octahedral group of order 48.

Links

• Wikipedia, Disdyakis dodecahedron
• Wikipedia, Truncated cuboctahedron

Crossrefs

Cf. A000332, A060530, A128766, A199406, A252704, A252705, A274900, A337963, A378473, A378475, A378476, A378477, A378478.

Formula

a(n) = (1/48)*(n^48 + 19*n^24 + 8*n^16 + 12*n^12 + 8*n^8).

Asymptotically, a(n) ~ n^48/48.