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Fibonacci Numbers

Tool to compute numbers of Fibonacci. Fibonacci sequence is a sequence of integers, each term is the sum of the two previous ones.

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Fibonacci Numbers -

Tag(s) : Mathematics

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# Fibonacci Numbers

## Fibonacci Numbers Calculator

### Display of the sequence

 Display of the sequence Around the last values Only the last number All the sequence (500 terms max)

### Initial values (seeds)

Tool to compute numbers of Fibonacci. Fibonacci sequence is a sequence of integers, each term is the sum of the two previous ones.

### How to calculate the Fibonacci sequence?

Numbers from the Fibonacci sequence are equal to the addition of the 2 previous terms, they follow the recurrence formula: $$F(n+2) = F(n) + F(n+1)$$

To initiate the sequence, take F(0) = 0 and F(1) = 1

Example: F2 = F0+F1 = 0+1 = 1
F3 = F1+F2 = 1+1 = 2
F10 = F8+F9, etc.

### What are the first terms of the Fibonacci sequence?

 F(0)= 0 1 1 2 3 5 8 13 21 34 55

### What is the Fibonacci Rabbits' problem?

The rabbits' problem is a problem proposed by Fibonacci in 1200.

There is a rabbit couple (male + female) and every month a couple breeds and give birth to a new pair of rabbits which in turn can reproduce itself after 2 months. How many rabbits will be born after X months?

In the beginning there is 1 couple then

 1 month 1 couple two months 2 couples three months 3 couples 4 months 5 couples 5 months 8 couples 6 months 13 couples 7 months 21 couples 8 months 34 couples

Each month, the total number of rabbits is equal to the sum of the numbers of the previous two months because it is the number of existing rabbits (the previous month) plus the number of babies born from rabbits couples who have at least two months (hence the number of rabbits 2 months ago). The numbers found are the numbers of the Fibonacci sequence.