Analogy between Fibonacci and Chebyshev

Quick observation: I recently noticed that Chebyshev polynomials and Fibonacci numbers have analogous formulas.

The nth Chebyshev polynomial satisfies

for |x| >= 1, and the nth Fibonacci number is given by

There's probably a way to explain the similarity in terms of the recurrence relations that both sequences satisfy.

More on Chebyshev polynomials

• Yogi Berra and Chebyshev
• Product of Chebyshev polynomials
• The Brothers Markov

More on Fibonacci numbers

• Fibonacci formula for pi
• Inverse Fibonacci numbers
• Fibonacci numbers and numerical integration