- The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by the recurrence relation
$$u _ { n + 1 } = \left( u _ { n } \right) ^ { 2 } - 1 , \quad n \geq 1 .$$
Given that \(u _ { 1 } = k\), where \(k\) is a constant,
- find expressions for \(u _ { 2 }\) and \(u _ { 3 }\) in terms of \(k\).
Given also that \(u _ { 2 } + u _ { 3 } = 11\),
- find the possible values of \(k\).