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

1, 114, 3891, 29854, 87981, 143797, 170335, 177160, 178153, 178243, 178248, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249, 178249

Offset

1,2

Comments

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.

References

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

Links

Table of n, a(n) for n=1..31.

M. J. Dominus, Jyrki Lahtonen, Marko Riedel, Edge coloring of the cube

Marko Riedel, Maple code for standard Power Group Enumeration using the cycle indices of the slots and the action on the repertoire of colors.

Crossrefs

Cf. A060530.

Sequence in context: A220332 A162675 A221293 * A112485 A220685 A199249

Adjacent sequences: A306191 A306192 A306193 * A306195 A306196 A306197

Keyword

nonn

Author

Marko Riedel, Jan 28 2019

Status

approved