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A284747 Number of proper colorings of the 2n-gon with 2 instances of each of n colors under dihedral (rotational and reflectional) symmetry. 1
0, 1, 4, 54, 1794, 99990, 7955460, 848584800, 116816051520, 20167501253760, 4268024125243200, 1086711068022148800, 327759648421871635200, 115567595710587359539200, 47104362677165542792243200, 21978200228619432098036736000, 11639211300056830532862403584000, 6943663015969522875618267601920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..18.

Omar Sehlouli, Marko Riedel, Hexagon coloring

FORMULA

For n>=2, (1/4)(n-1)! + (1/4)n! + (1/(4n)) * Sum_{p=0..n} C(n,p) ((-1)^p/2^(n-p)) ((2n-p)! + p(2n-p-1)!).

EXAMPLE

When n=2 the coloring of the nodes of the square with two instances each of black and white must alternate and a rotation by Pi/4 takes one coloring to the other, so there is just one coloring.

CROSSREFS

Cf. A274634, A284664.

Sequence in context: A201731 A225823 A265004 * A003955 A182264 A094154

Adjacent sequences:  A284744 A284745 A284746 * A284748 A284749 A284751

KEYWORD

nonn

AUTHOR

Marko Riedel, Apr 01 2017

STATUS

approved

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Last modified May 26 09:12 EDT 2017. Contains 287093 sequences.