Triangular Numbers which are also Square

Theorem
Let $A_n$ be the $n$th non-negative integer whose square is also a triangular number.

Then:
 * $A_n = \begin{cases} 0 & : n = 0 \\

1 & : n = 1 \\ 6 A_{n - 1} - A_{n - 2} & : n > 1 \end{cases}$