費氏數列由0和1開始，之後的費式係數就是由之前的兩數相加而得出，即
 F(0) = 0
 F(1) = 1
 F(n) = F(n – 1) + F(n – 2) (n >= 2)
所以前幾項的費式係數為0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,…

定義F^m(n) = F(…(F(n))的值 (m>=1)，如F¹(n) = F(n)，F²(n) = F(F(n))，F³(n) = F(F(F(n)))。當m=2, n=2時，F²(2) = F(F(2)) = F(F(1)+ F(0)) = F(1+0) = F(1) = 1，當m=2, n=3時，F²(3) = F(F(3)) = F(F(2)+ F(1)) = F(1+1) = F(2) = 1。當m=3, n=2時，F³(2) = F(F(F(2))) = F(F(1)) = F(1) = 1，而當m=3, n=3時，F³(3) = F(F(F(3))) = F(F(2)) = F(1) = 1。