A378475 The number of n-colorings of the vertices of the snub cube up to rotation.

0, 1, 700688, 11768099013, 11728130343936, 2483526957328125, 197432556580265616, 7982551312716034313, 196765270145344012288, 3323601794975613468921, 41666666667041700250000, 410405528159827444816781, 3312368633477962187301888, 22616698765607508420521013

Offset: 0

Author

Peter Kagey, Nov 27 2024

Keywords

• nonn

Comments

Equivalently, the number of n-colorings of the faces of the pentagonal icositetrahedron, which is the polyhedral dual of the snub cube.

Colorings are counted up to the rotational octahedral symmetry group of order 24.

This is also:

1) The number of n-colorings of the vertices of the truncated octahedron (equivalently faces of the tetrakis hexahedron) up to rotational octahedral symmetry (alternatively full tetrahedral symmetry).

2) The number of n-colorings of the vertices of the truncated cube (equivalently faces of the triakis octahedron) up to rotational octahedral symmetry.

Links

• Wikipedia, Pentagonal icositetrahedron
• Wikipedia, Snub cube

Crossrefs

Cf. A000332, A060530, A128766, A199406, A252704, A252705, A274900, A337963, A378473, A378474, A378476, A378477, A378478.

Formula

a(n) = (1/24)*(n^24 + 9*n^12 + 8*n^8 + 6*n^6).

Asymptotically, a(n) ~ n^24/24.