Other Concatenations

Here is a concatenation table to get all of the colorings of a row of three squares.  We used the results of the two-square concatenations to get the column headings for this table:

o	bb	bg	gb	gg
b	bbb	bbg	bgb	bgg
g	gbb	gbg	ggb	ggg

Notice that we have 2^3 = 8 different results.

We can create all the possible colorings of four squares by creating a table with 8 columns and concatenating each string with either a or b.  Or we could use the results of the 2-square table like this:

o	bb	bg	gb	gg
bb	bbbb	bbbg	bbgb	bbgg
bg	bgbb	bgbg	bggb	bggg
gb	gbbb	gbbb	gbgb	gbgg
gg	ggbb	ggbg	gggb	gggg

If we continue this process until we get strings of 9, how many strings do we end up with? 

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