What is a mathematical expression for the sequence $$2,0,1,7,8,8,2,0,1,7,8,8,2,0,1,7,8,8,...$$
Like this Following it's not I want to answer $$a_{n}=\begin{cases} 2&n=6k\\ 0&n=6k+1\\ 1&n=6k+2\\ 7&n=6k+3\\ 8&n=6k+4\\ 8&n=6k+5 \end{cases}$$
such this:simple expression
A generating function could be $g(x)=\dfrac{2+x^2+7x^3+8x^4+8x^5}{1-x^6}$
so the $n$th term of the sequence is the coefficient of $x^n$ in the expansion of $g(x)$, which can be found by dividing the $n$th derivative of $g(x)$ at $x=0$ by $n!$, i.e. $\dfrac{g^{(n)}(0)}{n!}$
A DFT (discrete fourier transform) gives $$a_k={13\over3}-{2\over3}(-1)^k-{11\over6}\cos{k\pi\over3}-{5\sqrt{3}\over2}\sin{k\pi\over3}+{1\over6}\cos{2k\pi\over3}-{\sqrt{3}\over6}\sin{2k\pi\over3}\ .$$
You can use $$-\frac13\left(13\cos\left(\frac\pi3n\right) + 15\cos\left(\frac\pi3\left(n-2\right)\right) + 2\cos\left(\pi n\right) + \cos\left(\frac{2\pi}3\left(n-1\right)\right) - 13\right).$$
