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

0,3

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

Table of n, a(n) for n=0..8.

Wikipedia Disdyakis dodecahedron

Wikipedia Truncated cuboctahedron

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.

Crossrefs

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

Sequence in context: A204349 A351171 A094910 * A295353 A210588 A023051

Adjacent sequences: A378468 A378469 A378473 * A378475 A378476 A378477

Keyword

nonn,easy,new

Author

Peter Kagey, Nov 27 2024

Status

approved