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

0,3

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

Table of n, a(n) for n=0..7.

Wikipedia, Pentagonal hexecontahedron

Wikipedia, Snub dodecahedron

Formula

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

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

Crossrefs

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

Sequence in context: A185434 A172655 A288287 * A349030 A083216 A180703

Adjacent sequences: A378475 A378476 A378477 * A378479 A378480 A378481

Keyword

nonn

Author

Peter Kagey, Nov 27 2024

Status

approved