Chapter 3: The World of Simple Programs

Section 5: Substitution Systems

Lucas numbers

Lucas numbers Lucas[n] satisfy the same recurrence relation f[n_]:=f[n-1]+f[n-2] as Fibonacci numbers, but with the initial conditions f[1]=1; f[2]=3. Among the relations satisfied by Lucas numbers are:


GoldenRation==(Lucas[n]+Fibonacci[n] Sqrt[5])/2

From Stephen Wolfram: A New Kind of Science [citation]