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
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