Let me know please, why i should not think in this way -

i have A ways to make n-1 strip sequences. If i will add red or white strip from the
left side, i have A ways to make n strip sequences.

        R/W + [n-1.....]

But in the same time i can add red or white strip from the right side, and so i'll have another
A ways to make n strip sequences.

        [n-1....] + R/W

So, now i have 2*A ways to make n strip sequences.

What's wrong in this kind of argumentation ?

Some ways may be counted twice, so the ways will be less than 2A