A378473 - OEIS

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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

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OFFSET

0,3

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

Table of n, a(n) for n=0..13.

Wikipedia, Tetrakis hexahedron

Wikipedia, Truncated octahedron

FORMULA

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