How to solve this functional (recurrence) equation ?

[jk22]

I'm in a problem where I have to solve the following functional equation :

F(n)^2=n+F(n+1)

Does anyone know some methods to solve this kind of problems ?

A similar equation happens in Ramanujan example of root denesting : http://en.wikipedia.org/wiki/Nested_radical#Square_roots

 

[mathman]

Don't know of a method. As stated the problem is incomplete - you need an initial condition (F(0) = ?).

 

[jk22]

The problem is to find F(1), knowing that F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}.

 

[Mentallic]

The problem is to find F(1), knowing that F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}.

Should that be to find F(n) given that F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}} ?

Find F(2) and the pattern becomes clear.