A284664 Number of proper colorings of the 2n-gon with 2 instances of each of n colors under rotational symmetry.

0, 1, 5, 96, 3528, 199620, 15908400, 1697149440, 233631921600, 40335000693120, 8536048230528000, 2173422135804796800, 655519296840629760000, 231135191421131129932800, 94208725354330431747302400, 43956400457238853734678528000, 23278422600113660887881093120000

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Omar Sehlouli, Marko Riedel, Hexagon coloring

Marko Riedel, Image of the five colorings of the hexagon (n=3).

Formula

For n>=2, (1/2)(n-1)! + (1/(2n)) * 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, A284747.

Sequence in context: A194616 A285367 A208253 * A194609 A139950 A102734

Adjacent sequences: A284661 A284662 A284663 * A284665 A284666 A284667

Keyword

nonn

Author

Marko Riedel, Mar 31 2017

Status

approved