F(k*n) = L(k)*F(k*(n-1)) - ((-1)**k)*F(k*(n-2))

##</code><code>##

L(k) = F(n-1) + F(n+1)

##</code><code>##

F(k*n) = (F(n-1)+F(n+1))*F(k*(n-1)) 
          - ((-1)**k)*F(k*(n-2))

##</code><code>##

F(n**2) = (F(n-1)+F(n+1))*F(n*(n-1)) 
          - ((-1)**n)*F(n*(n-2))

##</code><code>##

F(2*k+1) = F(k+1)**2 + F(k)**2