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Algebra Level 5

\[\large{{ a }_{ n+1 }={ \left( \left\lfloor \sqrt { \left\lfloor { a }_{ n } \right\rfloor -\left\lfloor \sqrt { { a }_{ n } } \right\rfloor } \right\rfloor \right) }^{ 2 }}\]

Define the recurrence relation as above, with an initial condition that \( a_{33} = 1 \). Determine \({ \left( \left\lfloor \sqrt { { a }_{ 2 } } \right\rfloor +1 \right) }^{ 2 } + { \left( \left\lfloor \sqrt { { a }_{ 2 } } \right\rfloor \right) }^{ 2 }\).

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