The sequence $ a_n$ satisfies $ a_{m+n}+ a_{m-n}=\frac12(a_{2m}+a_{2n})$ for all $ m\geq n\geq 0$. If $ a_1=1$, find $ a_{1995}$.
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Tags: induction, algebra proposed, algebra
The sequence $ a_n$ satisfies $ a_{m+n}+ a_{m-n}=\frac12(a_{2m}+a_{2n})$ for all $ m\geq n\geq 0$. If $ a_1=1$, find $ a_{1995}$.