Consider a stripe of n fieds, numbered from left to right with the integers 1 to n in ascending order. Each of the fields is colored with one of the colors 1, 2 or 3. Even-numbered fields can be colored with any color. Odd-numbered fields are only allowed to be colored with the odd colors 1 and 3.
How many such colorings are there such that any two neighboring fields have different colors? inductioncombinatorics proposedcombinatorics