

A185437


The least number of colors required to color an nbead necklace so that each bead can be identified.


1



1, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
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OFFSET

1,2


COMMENTS

In other words, the least number of colors in any coloring of the necklace that is not symmetric under any element of the corresponding dihedral group.


LINKS



FORMULA

a(n) = 2 for all n > 5.
G.f.: x*(x^2+1)*(x^3x1)/(x1). [Colin Barker, Oct 26 2012]


EXAMPLE

For n=5, one coloring is ABBCC. Any coloring using two symbols will have two indistinguishable beads.
For n > 5, a coloring is ABAAB...B, where ... is zero or more B's. We can tell the A's apart because one has a B on either side, of the other two one is closer to the single B, and one is closer to the long sequence of B's. Of the B's, one has an A on either side. The remaining B's can be distinguished by counting along the string of B's starting at the end with a singleton A.


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



