What is the next number in the sequence?

[aykantspel]

2, 2, 8, 72, 392, 2312, ?

The sequence can be represented visually by the attached image.

The smallest rectangles are 2x1. Every rectangle has a 2:1 ratio. Each number in the sequence represents the area of each successively larger rectangle.

I can figure out the next number, but I can't figure out how to represent it mathematically.

 

[CompuChip]

Welcome to PF aykantspel.

Suppose that you have somewhere a rectangle with sides of length L and 2L. Possibly looking at the picture, can you say in terms of L what the sides of the next bigger rectangle will be?

You can start by drawing an example: if L = 1 you start with a 2 x 1 rectangle, what will be the size of the next?