Fibonacci sequence

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The numbers satisfying: LaTeX: F_{n+2} = F_{n+1} + F_n, with initial conditions LaTeX: F_0 = F_1 = 1. As shown in the following table, the fibonacci sequence grows rapidly after LaTeX: N=10, and LaTeX: F_N becomes astronomical for LaTeX: N > 50,

         N    F_N
       ==============
         0      1
         1      1
         2      2
         3      3
         4      5
         5      8
         6     13
         7     21
         8     34
         9     55
        10     89
        20  10946
        50    2.0E10
       100    5.7E20
      ==============     

Named after the 13th century mathematician who discovered it, this sequence has many interesting properties, notably for an optimal univariate optimization strategy, called fibonacci search.


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