I have another question about sequences.

On the previous question, we had found an explicit formula even for any n a natural number (there were conditions on the formula, if n was odd or even).

Now I asked myself the following question:

Give an explicit formula of U(n) for any n on the natural integers such as:

If n = 0 mod 3, U(n)=(7/3)n+1

If n = 1 mod 3, U(n)=(7/3)n+5/3

If n = 2 mod 3, U(n)=(7/3)n+8/3

I wanted to use the cosine function but I don't know how to search well enough to find 3 values that repeat.

There is another one which is easier to find.

Okay so I found something !