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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is suitable to you.
A slightly different but very close problem is discussed at
You might want to check it out, before looking at ...
The two pages solution explains in detail how to build and solve the recurrence relations that describes the system.