Iteration of a recurrence solution in R

Question

I'm given a question in R language to find the 30th term of the recurrence relation x(n) = 2*x(n-1) - x(n-2), where x(1) = 0 and x(2) = 1. I know the answer is 29 from mathematical deduction. But as a newbie to R, I'm slightly confused by how to make things work here. The following is my code:

loop <- function(n){
  a <- 0
  b <- 1
  for (i in 1:30){
    a <- b
    b <- 2*b - a
  }
  return(a)
}

loop(30)

I'm returned 1 as a result, which is way off.

In case you're wondering why this looks Python-ish, I've mostly only been exposed to Python programming thus far (I'm new to programming in general). I've tried to check out all the syntax in R, but I suppose my logic is quite fixed by Python. Can someone help me out in this case? In addition, does R have any resources like PythonTutor to help visualise the code execution logic?

Thank you!

question from:https://stackoverflow.com/questions/65872550/iteration-of-a-recurrence-solution-in-r

Answer 1

I guess what you need might be something like below

loop <- function(n){
  if (n<=2) return(n-1)
  a <- 0
  b <- 1
  for (i in 3:n){
    a_new <- b
    b <- 2*b - a
    a <- a_new
  }
  return(b)
}

then

> loop(30)
[1] 29

---

If you need a recursion version, below is one realization

loop <- function(n) {
  if (n<=2) return(n-1)
  2*loop(n-1)-loop(n-2)
}

which also gives

> loop(30)
[1] 29