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Is Maple's answer correct?

Michael 222
April 09 2007
0
Hi: Procedure "rsolve" in both Maple 10 (and 11) gives a complicated answer to the following recursion: rs:=subs(n=n,4*(n-1)^2*f(n-2)-(3+8*n^2-8*n)*f(n-1)+4*f(n)*n^2); ans:=rsolve({rs=0,f(1)=3/4,f(2)=41/64},{f(k)}); The answer involves both indices "n" and "k". I tried testing the answer by checking the original recursion equation and it doesn't work. (I am not posting the answer, but you can generate it by yourself by pasting the code above) Questions: 1. What does it mean when a recursion solution involves TWO indices? An example similar to this case is given in the help file, but the answer only involves one index. 2. Is the complicated answer correct? If so, can anyone show how to make it satisfy the original recursion equation? Thanks Michael PS. I tried this on Maple support a couple of weeks ago, and got no response.
testing example

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