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We have two types of shapes.

Using these shapes we need to construct $2$*$x$ shapes (height is 2 units and width is $x$ units).

For example, all $5$ possible constructions of $2$*$2$ area are shown below,

And following is one possible construction of $2$*$4$ area,

Now if $h_x$ is the no of possible arrangements for an area of $2$*$x$ $\text{unit}^2$ , where $x$ = $0$,$1$,$2$,$3$,$4$.....$\infty$, then find $G(x)$ corresponding to <$h_0$,$h_1$,$h_2$,$h_3$...>