[ [ Linear Recurrence Relations ]

Calculate the sum: $S_{n}=C_{n}^{0}-C_{n-1}^{1}+C_{n-2}^{2}-\ldots$.

#
Just like in problem $\underline{60581}$, it is checked that $S_{0}=S_{1}=1, S_{n}=S_{n-1}-S_{n-2}$ for $n \geq 3$.

## Answer

$S_{n}=0$, if $n \equiv 2,5(\bmod 6) ; S_{n}=1$, if $n \equiv 0,1(\bmod 6) ; S_{n}=-1$, if $n \equiv 3,4(\bmod 6)$.