Definition:Square Number/Definition 2

Definition
Square numbers are defined as:
 * $S_n = \begin{cases}

0 & : n = 0 \\ S_{n-1} + 2 n - 1 & : n > 0 \end{cases}$ for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Square Number