$a_{n,3}$
$1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,\cdots \cdots $
$a_{n,5}$
$1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,\cdots \cdots $
$a_{n,7}$
$1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,\cdots \cdots $
$\vdots $
$a_{n,2k+1}$
$1,\cdots \cdots\cdots \cdots,1,\cdots \cdots\cdots \cdots,\overbrace{1,\cdots \cdots\cdots \cdots}^{2k+1},1,\cdots \cdots\cdots \cdots,1,\cdots \cdots$
I found $a_{n,k}= \left \lfloor \left | \cos\frac{\pi (n-1)}{2k+1} \right | \right \rfloor$ but this term include abs and floorfucntion.
I mean i want the General Term without abs and floorfucntion.(plus sum)
Any hints will be appreciated, thank you.