Notes

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:

Lucas[n_] := Fibonacci[n - 1] + Fibonacci[n + 1]

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



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