(1) Dynamic programming
L(i)=2
for i=0
L(i)=1
for i=1
L(i)=L(i-2)+L(i-1) for i=2,3,4,. . .
(2) General form
where 
is Golden ratio.
Ratio L(n+1)/L(n) approaches Golden ratio as n increases.
Golden ration 
is a positive root of 
.
fib(n-1)+fib(n+1)=L(n)
fib(2*n)=L(n)*fib(n)
fib(n)=(L(n-1)+L(n+1))/5
The plot of 
