Squares in Fibonacci-like sequences After the answers to my last question, I wonder if there is any sequence of the form  $A_0=0$, $A_1=1$, $$A_{n+2}=pA_{n+1}-qA_{n}$$ where $p$ and $q$ are fixed integers which contains infinitely many different square numbers.

You can take $p=2,q=1$, then $A_n=n$ for all $n$, and it follows that it is a square infinitely often.
