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  1. or download this
    F(n+m) = F(n)F(m-1) + F(n-1)F(m+1)
  2. or download this
    F(2n) = F(n)F(n-1) + F(n-1)F(n+1)
      = F(n)F(n-1) + F(n-1)(F(n) + F(n-1))
      = 2F(n)F(n-1) + F(n-1)F(n-1)
  3. or download this
    F(2n-1) = F(n-1)F(n-1) + F(n-2)F(n)
        = F(n-1)F(n-1) + (F(n)-F(n-1))F(n)
        = F(n)F(n) - F(n-1)F(n) + F(n-1)F(n-1)