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1. Sequence with a quadratic shift relation ●●●○○ 50 ptsLet the sequence $a_0, a_1, a_2, \ldots$ satisfy $a_0=a_1=11$ and $a_{m+n}=\frac{1}{2}\left(a_{2m}+a_{2n}\right)-(m-n)^2$ for all integers $m, n \geqslant 0$. Find $a_{45}$.