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A356685
Number of inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using at most n colors.
1
1, 2802752, 105912891117, 187650085502976, 62088173933203125, 7107572036889562176, 391145014323085681337, 12592977289302016786432, 269211745393024690982601, 4166666666704170025000000
OFFSET
1,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Marko Riedel, Aug 22 2022
STATUS
approved