Fibonacci Numbers & Sequence

Fibonacci sequence is a sequence of numbers, where each number is the sum of the 2 previous numbers, except the first two numbers that are 0 and 1.

Fibonacci sequence formula

For example:

F0 = 0

F1 = 1

F2 = F1+F0 = 1+0  = 1

F3 = F2+F1 = 1+1  = 2

F4 = F3+F2 = 2+1  = 3

F5 = F4+F3 = 3+2  = 5

...

Golden ratio convergence

The ratio of two sequential Fibonacci numbers, converges to the golden ratio:

\lim_{n\rightarrow \infty }\frac{F_n}{F_{n-1}}=\varphi

φ is the golden ratio = (1+√5) / 2 ≈ 1.61803399

Fibonacci sequence table

n Fn
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
17 1597
18 2584
19 4181
20 6765

Fibonacci sequence calculator

TBD

C code of Fibonacci function

double Fibonacci(unsigned int n)

{

    double f_n =n;

    double f_n1=0.0;

    double f_n2=1.0;

 

    if( n > 1 ) {

        for(int k=2; k<=n; k++) {

            f_n  = f_n1 + f_n2;

            f_n2 = f_n1;

            f_n1 = f_n;

        }

    }

 

    return f_n;

}

 

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