Alternating multiplier recurrence for convergents of the square root of eleven
= Alternating multiplier recurrence for convergents of the square root of eleven
If $p_n/q_n$ are the convergents of $\sqrt{11}$, then
$$
p_{n+1}+q_{n+1}\sqrt{11}
=\begin{cases}
(3+\sqrt{11})(p_n+q_n\sqrt{11}),&n\text{ odd},\\
\dfrac{3+\sqrt{11}}2(p_n+q_n\sqrt{11}),&n\text{ even}.
\end{cases}
$$