A378475 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

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

Wikipedia, Pentagonal icositetrahedron

Wikipedia, Snub cube

FORMULA

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

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

CROSSREFS

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

Sequence in context: A258129 A204496 A332850 * A183835 A273969 A203834

Adjacent sequences: A378472 A378473 A378474 * A378476 A378477 A378478

KEYWORD

nonn

AUTHOR

Peter Kagey, Nov 27 2024

STATUS

approved