project euler problem 463

A weird recurrence relation  

 I did not solve any PE problems recently because my work kept me very busy and I read some books recently such as Richard Stanley's famous book  Enumerative Combinatorics. It is an excellent book, but it takes a lot of time, the problems at the end of each chapter are very challenging!

 Just a couple days ago, I took a look at recent PE problems and found some of the problems are quite simple, for example, problem 463. 

This problem is not interesting at all. The recurrent equations looks difficult to human beings, but it is trivial for computers. After half an hour's coding and a few minutes debugging, the problem is solved!