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

0,3

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

Table of n, a(n) for n=0..5.

Wikipedia, Disdyakis triacontahedron

Wikipedia, Truncated icosidodecahedron

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

Crossrefs

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

Sequence in context: A115532 A074194 A135386 * A095462 A115543 A219323

Adjacent sequences: A378474 A378475 A378476 * A378478 A378479 A378480

Keyword

nonn

Author

Peter Kagey, Nov 27 2024

Status

approved