What is this exercise asking us to do?

[Arslan7041]

What is exercise #7 in this link asking us to do? http://en.wikibooks.org/wiki/C%2B%2B_Programming/Exercises/Iterations

Write a program that asks the user to type an integer N and compute u(N) defined with :
u(0)=3
u(n+1)=3*u(n)+4

Im unfamiliar with this notation. Does this have something to do with discrete math?

[Ispil]

It's a recursive series. The way it works is this: you are given the initial value (u(0)=3) and, when asked to find the next value (u(1)), you must use the value generated before to find the new value. For example, u(1) = u(0+1) = 3*u(0)+4 = 13. u(2) = u(1+1) = 3*u(1)+4 = 43. So on and so forth.

[Arslan7041]

I think I get it. But how do I know when to end this recursive program? I mean, it doesn't tell us when to end it. Should I just pick an arbitrary number of recursions to end at?

[BlatantlyX]

It will end when u(0) is reached, which returns 3. eg.
u(2) will call u(1) which will call u(0), each using the returned value in its equation.

[Ispil]

Just think of it like making a Fibonacci calculator, except instead of adding the previous term, also multiply it by 3 and add 4.

[Arslan7041]

Alright, played around with it a little but I think I got it. Can someone test it out a confirm?

#include <iostream>
using namespace std;

int rec (int N)
{
    if(N==0)
        return 3;
    else if (N>0)
        return 3*rec(N-1)+4;
}

int main ()
{
    int N;
do{
    cout << "Please enter an integer N: " << flush;
    cin >> N;
   
 if(N==0)
        cout << "u(0) = " << rec(N) << endl;
    else
    cout << "u(" << N << ") = " << rec(N) << endl;
    cout << "\n";
    } while(N!=-1);

    return 0;
}

Thank you everyone for your input. I appreciate it :)

[BlatantlyX]

I can confirm that this works for positive integers.