Fibonacci(n)

Fibonacci(0)                            # 1
Fibonacci(2)                            # 2
Fibonacci(0:3)                          # 0 1 1 2


# Golden ratio
F <- Fibonacci(1:25)                    # ... 75025 121393
f25 <- F[25]/F[24]                      #     1.618033989
phi <- (sqrt(5) + 1)/2
abs(f25 - phi)                          # 7.945178e-11

# Fibonacci numbers without iteration
fibo <- function(n) {
  phi <- (sqrt(5) + 1)/2
  fib <- (phi^(n+1) - (1-phi)^(n+1)) / (2*phi - 1)
  round(fib)
}
  
fibo(30:33)                             # 1346269 2178309 3524578 5702887