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For a sequence $\{D_k\}$, if we have: $$D_k=pD_{k+1}+qD_{k-1}+1$$

and we know that $D_0=D_N=0$. Where $p+q=1$, and $N$ is known. How do I solve it?

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    [Here](http://math.stackexchange.com/questions/205372/how-to-solve-this-recurrence-relation-f-n-3f-n-1-12-1n/205491#205491) is a related problem.2012-11-04
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    I would use a generating function: Let $d(x) = \sum x^k D_k$, apply the recurrence and end conditions, and see what happens.2012-11-04

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