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文 [1]得到Tn=cosn2π7+cosn 4π7+cosn 6π7的一个递归式 :Tn+ 3 =- 12 Tn+ 2 +12 Tn + 1 +18Tn.本文给出 {Tn}的一个通项公式Tn=- 12 +72 n k∈KCkn+[1+( - 1) n] 72 n+ 2 C[n2 ] n ,( )其中K ={k|n - 2k =7m ,0≤k≤ [n - 12
In [1], a recursive formula of Tn=cosn2π7+cosn4π7+cosn6π7 is obtained: Tn+3 =- 12 Tn+ 2 +12 Tn + 1 +18Tn. This paper gives a general formula of {Tn} Tn=- 12 +72 n k∈KCkn+[1+( - 1) n] 72 n+ 2 C[n2 ] n ,( ) where K ={k|n - 2k =7m, 0≤k≤ [n - 12