color flags

We want to design a flag with these terms:
1. It should be ribbed, contains 3 coloumns. Coloumns can be green, red and white.
2. Same color coloumns shouldn't putted beside each other.
3. White flags always should be between green and red or red and green coloumns.

How many flags it is possible to design by above rules for N coloumns?

For example for N=3 flags are :

sb1370 said:

We want to design a flag with these terms:
1. It should be ribbed, contains 3 coloumns. Coloumns can be green, red and white.
2. Same color coloumns shouldn't putted beside each other.
3. White flags always should be between green and red or red and green coloumns.

How many flags it is possible to design by above rules for N coloumns?

For example for N=3 flags are :

Click to expand...

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Sorry, you're right.
This question is a part of a problem.
TA said it can be solved by recursive relations.