A378473 The number of n-colorings of the vertices of the truncated octahedron up to rotation and reflection.

0, 1, 355048, 5886817533, 5864336054656, 1241773051013125, 98716454926955496, 3991277735434713913, 98382652674879674368, 1661801013342756245961, 20833333958666683585000, 205202766952229526577141, 1656184328295547539616128, 11308349424395689922231053

Offset: 0

Author

Peter Kagey, Nov 27 2024

Keywords

• nonn

Comments

Equivalently, the number of n-colorings of the faces of the tetrakis hexahedron, which is the polyhedral dual of the truncated octahedron.

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

Links

• Wikipedia, Tetrakis hexahedron
• Wikipedia, Truncated octahedron

Crossrefs

Cf. A000332, A060530, A128766, A199406, A252704, A252705, A274900, A337963, A378474, A378475, A378476, A378477, A378478.

Formula

a(n) = (1/48)*(n^24 + 3*n^16 + 16*n^12 + 8*n^8 + 12*n^6 + 8*n^4).

Asymptotically, a(n) ~ n^24/48.