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%I #20 Aug 24 2022 09:31:33
%S 1,2802752,105912891117,187650085502976,62088173933203125,
%T 7107572036889562176,391145014323085681337,12592977289302016786432,
%U 269211745393024690982601,4166666666704170025000000
%N Number of inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using at most n colors.
%H Marko Riedel et al., Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/4516333/">Coloring faces, vertices, edges of a cube</a>.
%F a(n) = (1/24)*(n^26 + 9*n^14 + 8*n^10 + 6*n^8).
%F Cycle index is (1/24) * (x1^26 + 6*x1^2*x4^6 + 9*x1^2*x2^12 + 8*x1^2*x3^8).
%Y Cf. A355502.
%K nonn,easy
%O 1,2
%A _Marko Riedel_, Aug 22 2022