Ring my Bell, Ring my Bell
\(4\) has the property that if one adds it to double its square, it yields a perfect square. In other words for natural numbers \(m,n\):
\[n^2 + n^2 + n = m^2 \]
There are four such \(n<10^6 \). If \(4\) is the smallest \(n\), what is the second smallest \(n\)?