A284747 Number of proper colorings of the 2n-gon with 2 instances of each of n colors under dihedral (rotational and reflectional) symmetry.

0, 1, 4, 54, 1794, 99990, 7955460, 848584800, 116816051520, 20167501253760, 4268024125243200, 1086711068022148800, 327759648421871635200, 115567595710587359539200, 47104362677165542792243200, 21978200228619432098036736000, 11639211300056830532862403584000, 6943663015969522875618267601920000

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 A355128

Adjacent sequences: A284744 A284745 A284746 * A284748 A284749 A284750

Keyword

nonn

Author

Marko Riedel, Apr 01 2017

Status

approved