===== Fibonacci =====

  * [[http://forums.xkcd.com/viewtopic.php?t=57306&p=2039068|Lagged fibonacci]]

----

<m 16>
{matrix{3}{1}
{
  {F_1 = 0}
  {F_2 = 1}
  {F_n = F_{n-1} + F_{n-2}}
}}
</m>
----
<m 16>
{matrix{2}{1}
{
   {varphi={1+sqrt 5}/2}
   {F_{n}={varphi^n-( -varphi)^-n}/sqrt 5}
}}
</m>
----
<m 16>
{matrix{3}{1}
{
  {F_{2n} = {F_n}^2+{F_{n+1}}^2}
  {F_{2n+1} = (2F_n+F_{n+1})F_{n+1}}
  {F_{2n-1} = (2F_{n+1}-F_n)F_n}

}
}
</m>
----
<m 16>
{matrix{2}{2}
{
  {for n ulige}{F_{n} = {(F_{{n-1}/2}})^2+{(F_{{n+1}/2}})^2} 
  {for n lige}{F_{n} = (2F_{n/2-1}+F_{n/2})F_{n/2}}

}
}
</m>
----
Formula til non-Fibonacci tal:
<m>
floor ( n + log_varphi (sqrt 5(log_varphi(n sqrt{5})+n)−5+{3}/n)−2 ) for n>=2 
</m>