Fibonacci functions

Fibonacci functions - Fibonacci functions are represented as Fn = Fn-1 + Fn-2; where F denotes a function followed by a subscripted symbolization of its iteration. They can be alternately elucidated as 'a generalized form of Fibonacci numbers'. However, for reporting the magnitude for the nth term, adding the numbers iteratively may produce an uphill task (especially in cases where n is very large). Therefore, a special function has been devised to resolve this impediment, given by: an = [ Phin - (phi)n]/Sqrt[5]; where Phi = (1+Sqrt[5])/2.