

A284747


Number of proper colorings of the 2ngon 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
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OFFSET

1,3


LINKS



FORMULA

For n>=2, (1/4)(n1)! + (1/4)n! + (1/(4n)) * Sum_{p=0..n} C(n,p) ((1)^p/2^(np)) ((2np)! + p(2np1)!).


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



KEYWORD

nonn


AUTHOR



STATUS

approved



