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
Keywords
Examples
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.
Links
- 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)!).