Is there any way to optimize this function and make it faster?

is there a way to optimize this? It is taking way too long to run

let counter2 = ref 0

let rec s2 num = 
  counter2 := !counter2 + 1;
  match num with
  | 0 -> 1
  | 1 -> 2
  | _ -> (((((6*num)-3) * (s2 (num-1))) / (num+1))) - (((num-2)* (s2 (num-2))/(num+1)))

Here is the highly recursive definition of the Fibonacci sequence:

let rec fib n = 
  if n < 2 then n 
  else fib (n - 2) + fib (n - 1)

Here is the not so recursive definition of the Fibonacci sequence.

let nfib n =
  let rec helper pprev prev i =
    if i = n then
      pprev + prev
    else
      helper prev (pprev + prev) (i + 1)
  in
  if n < 2 then n 
  else helper 0 1 2

Here is a function for timing things:

let time f x =
  let st = Unix.gettimeofday () in
  let res = f x in
  Printf.printf "%f seconds\n" (Unix.gettimeofday () -. st);
  res

Here are times for the fib and nfib functions:

# time fib 42;;
7.694294 seconds
- : int = 267914296
# time nfib 42;;
0.000002 seconds
- : int = 267914296