Definition:Square Number/Definition 2
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Definition
Square numbers are defined as:
- $S_n = \begin {cases} 0 & : n = 0 \\ S_{n - 1} + 2 n - 1 & : n > 0 \end {cases}$
for $n = 1, 2, 3, \ldots$
Examples of Square Numbers
The first few square numbers are as follows:
Sequence of Square Numbers
The sequence of square numbers, for $n \in \Z_{\ge 0}$, begins:
- $0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, \ldots$