观察下列等式：由以下等式推测到一个一般的结论：对于\(n\in {{N}^{*}}\)，\({C}_{4n+1}^{1}+{C}_{4n+1}^{5}+{C}_{4n+1}^{9}+\cdots +{C}_{4n+1}^{4n+1}=\)      _________  ．

\({C}_{5}^{1}+{C}_{5}^{5}={{2}^{3}}-2\)，

\({C}_{9}^{1}+{C}_{9}^{5}+{C}_{9}^{9}={{2}^{7}}+{{2}^{3}}\)，

\({C}_{13}^{1}+{C}_{13}^{5}+{C}_{13}^{9}+{C}_{13}^{13}={{2}^{11}}-{{2}^{5}}\)，

​\({C}_{17}^{1}+{C}_{17}^{5}+{C}_{17}^{9}+{C}_{17}^{13}+{C}_{17}^{17}={{2}^{15}}+{{2}^{7}}\)，

​\(………\)