Recurrence relations

[Cliff B]

I would be grateful if someone could point me in the direction of a
good book, or material on the web, on recurrence relations.

I'm interested in recurrences of the form

f_2(n)a_{n+2}+f_1(n)a_{n+1}+f_0(n)a_n=0

where f_k(n) is some simple polynomial in n. In
particular criteria for whether a_n converges, diverges or oscillates,
and if a_n diverges, whether a_{n+1}/a_n converges.

Thanks in advance for any help.