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  1. or download this
    F(k*n) = L(k)*F(k*(n-1)) - ((-1)**k)*F(k*(n-2))
  2. or download this
    L(k) = F(n-1) + F(n+1)
  3. or download this
    F(k*n) = (F(n-1)+F(n+1))*F(k*(n-1)) 
          - ((-1)**k)*F(k*(n-2))
  4. or download this
    F(n**2) = (F(n-1)+F(n+1))*F(n*(n-1)) 
          - ((-1)**n)*F(n*(n-2))
  5. or download this
    F(2*k+1) = F(k+1)**2 + F(k)**2