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I am stuck with computing n-th order difference equation:

$$ f(n) = \sum_{i=0}^{n-1} k(n-i)f(i) + B $$ where B is constant and k is a function dependent on $n$. Can I solve this equation explicitly or know some solution properties such as limiting behavior or boundness?

Thanks in advances.

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    Writing $F(n) = \sum_i f(i)$ makes it look more like a traditional difference equation. – 2017-02-16
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    Oh sorry, I typed the wrong equation and changed $k(n)$ to $k(n,i)$. This make the problem much diffucult. Thank you for your comment. – 2017-02-16
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    This is a linear equation with an inhomogeniety B. Hence there are standard methods to solve it. Hint: first think of what you can do to remove B, then let f = q^i and solve for q. It is highly recommended to start with small values of n. – 2017-02-16
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    @user155214 yes, you are right, constant coefficients are required for the power ansatz to work.. The example c(n) = n c(n-1) shows it. – 2017-02-16
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    @Dr. Wolfgang Hintze I appreciate for sparing your time. Can you reccomend some refrence for those context? – 2017-02-16

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