A356685 Number of inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using at most n colors.

1, 2802752, 105912891117, 187650085502976, 62088173933203125, 7107572036889562176, 391145014323085681337, 12592977289302016786432, 269211745393024690982601, 4166666666704170025000000

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Marko Riedel et al., Mathematics Stack Exchange, Coloring faces, vertices, edges of a cube.

Formula

a(n) = (1/24)*(n^26 + 9*n^14 + 8*n^10 + 6*n^8).

Cycle index is (1/24) * (x1^26 + 6*x1^2*x4^6 + 9*x1^2*x2^12 + 8*x1^2*x3^8).

Crossrefs

Cf. A355502.

Sequence in context: A250535 A203912 A355502 * A234189 A321056 A033534

Adjacent sequences: A356682 A356683 A356684 * A356686 A356687 A356688

Keyword

nonn,easy

Author

Marko Riedel, Aug 22 2022

Status

approved