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A306194 Non-isomorphic colorings of the edges of a cube using at most n colors under rotational symmetries and permutations of the colors. 1

%I #17 Jan 29 2019 19:31:19

%S 1,114,3891,29854,87981,143797,170335,177160,178153,178243,178248,

%T 178249,178249,178249,178249,178249,178249,178249,178249,178249,

%U 178249,178249,178249,178249,178249,178249,178249,178249,178249,178249,178249

%N Non-isomorphic colorings of the edges of a cube using at most n colors under rotational symmetries and permutations of the colors.

%C This uses Power Group Enumeration (PGE). The sequence ceases to grow once it reaches a(12) = 178249 because at most twelve colors can be represented and in a coloring with additional colors beyond the initial twelve the new colors can be permuted out and replaced by colors from the initial set, forming part of an orbit that has already been counted.

%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973.

%H M. J. Dominus, Jyrki Lahtonen, Marko Riedel, <a href="https://math.stackexchange.com/questions/150016/">Edge coloring of the cube</a>

%H Marko Riedel, <a href="/A306194/a306194_1.maple.txt">Maple code for standard Power Group Enumeration using the cycle indices of the slots and the action on the repertoire of colors.</a>

%Y Cf. A060530.

%K nonn

%O 1,2

%A _Marko Riedel_, Jan 28 2019

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