what is Fibonacci sequence

what is Fibonacci sequence

  2월 17, 2022    Eunhan's library

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Definition

Certain patterns of numbers.
first and second numbers are always 0,1. next number is addition of previous two numbers

The List of Fibonacci numbers

$0,1,1,2,3,5,8,13,21,34,55...$

Recurrence Relation

$F_0=0$
$F_1=1$
$F_n=F_{n-1}+F_{n-2}$

Example

index	fibonacci numbers	calculation
0	0	0
1	1	1
2	1	0+1
3	2	1+1
4	3	1+2
5	5	2+3
6	8	3+5
7	13	5+8
8	21	8+13
9	34	13+21
10	55	21+34
11	89	34+55
12	144	55+89
13	233	89+144
14	377	144+233
15	610	233+377
16	987	377+610