0

How does one solve a recurrence relation like

\begin{equation} a_n=\begin{cases} Pa_{n-1} + C , & a_{n-1}=7k, k \in \mathbb{N}, k\text{ is even}.\\ Qa_{n-1} + R , & a_{n-1} =7k, k \in \mathbb{N}, k \text{ is odd}. \end{cases} \end{equation}

I know how to solve homogenous recurrence relations and non-homogenous recurrence relations of order 2. But not when there are multiple cases in them like this. Any help?

William
  • 4,893
  • If anyone can point me to a method of finding a general solution for these little monsters, I'd appreciate it. – William Apr 03 '21 at 09:20
  • 1
    Are you familiar with the Collatz problem? That's similar to what you're asking about, and is an infamous unsolved problem. – Gerry Myerson Apr 03 '21 at 10:17
  • @Gerry Myerson Are you sure this thing is unsolved yet? I was fooling around with something and ended up with this. Well if it's unsolved, I guess I'll just leave it be and move on to other things :'( – William Apr 03 '21 at 12:14
  • I mean that Collatz is unsolved. I don't know how hard your question is, I'm just pointing out that it's outwardly similar to Collatz, so it might be a very difficult problem. – Gerry Myerson Apr 03 '21 at 22:33

0 Answers0