Task 501

The task

The hexagon with the R is colored red. Each hexagon is colored either red, yellow or green, such that no two hexagons with a common side are colored the same color. In how many different ways can the figure be colored? [asy] path a=(0,0)--(10,0)--(15,8.7)--(10,17.3)--(0,17.3)--(-5,8.7)--cycle; draw(a); draw(shift((15,8.7))*a); draw(shift((15,-8.7))*a); draw(shift((30,17.3))*a); draw(shift((30,0))*a); draw(shift((30,-17.3))*a); draw(shift((45,26))*a); draw(shift((45,8.7))*a); draw(shift((45,-8.7))*a); draw(shift((60,17.3))*a); draw(shift((60,0))*a); draw(shift((60,-17.3))*a); draw(shift((75,8.7))*a); draw(shift((75,-8.7))*a); label("$R$",(5,10),S); [/asy]