Possible Combinations

[OR_]

Hi!
I need help with the following question:
How many possible combinations are there to tile a road with n stones, colored red, blue, and yellow,
so that there will be no sequence of two stones of the same color?

What I did: the first stone can be either blue, red, or yellow, so it has 3 options. From the second stone onwards, there are only 2 options per stone,
because a stone cannot have the same color as the one before it. So in total, I have 3* 2^n-1 combinations.
I was wondering about the possibility that n=0, and that led me to think that maybe a recursive formula is necessary here.

I would be happy to hear your thoughts about this!
thanks

 

[Romsek]

[MATH]3\cdot 2^{n-1}[/MATH] looks correct to me.

[MATH]n[/MATH] is in the question. The tile sequence is [MATH]n[/MATH] stones long.

[MATH]n=0[/MATH] is a forbidden value. You obviously can't tile anything with zero tiles.