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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