4.
已知数列\(\{a_{n}\}\)满足\(a_{1}=m\), \(a_{n+1}=\begin{cases} 2a_{n}\mathrm{{,}}n{=}2k\mathrm{{-}}1\mathrm{{,}} \\ a_{n}{+}r\mathrm{{,}}n{=}2k \end{cases}(k∈N^{*},r∈R)\),其前\(n\)项和为\(S_{n}.\)若对任意的\(n∈N^{*}\),数列\(\{a_{n}\}\)都满足\(a_{n+2}=a_{n}\),则\(m\)与\(r\)满足的关系为____\(.\)