Also, and although it requires a bit more mathematics, it is possible to reduce some recurrences to a closed form, which allow the direct computation of the N-th term of a recurrence... That is also useful when the values of N are very large and one has doubts about the matrix ~~assemblation... ~~assemblation...As this was mentioned on the comments for the problem CROWD, I recommend everyone who is interested in reading more about "closing" recurrences, the following link:
http://hcmop.wordpress.com/2012/04/20/using-characteristic-equation-to-solve-general-linear-recurrence-relations/
Bruno