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Fibonacci Numbers

Fibonacci numbers in discrete mathematics are a sequence of numbers that satisfy a linear recurrence relation. The first few Fibonacci numbers are \(0,1,1,2,3,5,8,13,21,...\) By definition, the first two Fibonacci numbers are either \(0,1\) or \(1,1.\) 

As you can see, by adding the two previous consecutive numbers in the sequence, one can generate the next numbers in this sequence using this method. The general rule of the Fibonacci sequence satisfies the second-order recurrence relation pictured below:


Notice the starting values can be either \(F_0=0,F_1=1\) or \(F_1=1,F_2=1.\)        
The Fibonacci numbers have a closed formula called Binet’s Formula when \(n\ge0.\)