Define the sequences $\displaystyle x(n),y(n) $ by, $\displaystyle x(0)=0$, $\displaystyle x(n)=n-y(x(n-1)), \ y(n)=n-x(y(n-1))$ for $\displaystyle n \geq 1$. Determined closed expressions for these sequences.
Define the sequences $\displaystyle x(n),y(n) $ by, $\displaystyle x(0)=0$, $\displaystyle x(n)=n-y(x(n-1)), \ y(n)=n-x(y(n-1))$ for $\displaystyle n \geq 1$. Determined closed expressions for these sequences.