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I came across a linear recurrence with polynomial coefficients and realized that I don't have a clue as to how to solve it. The usual methods like generating functions or guessing seem not to work in that case.

Here is the equation:

[tex]

i (i - 1) (i - 2) b= 1/3 (i + 1) i (1 - i) b[i - 3] + (1 + i) i (i - 2) b[i - 2] + (i + 1) (i - 1) (i - 2) b[i - 1]

[/tex]

Is there any general theory on recursions of that type or maybe even a general algorithm to compute the solution (in terms of some initial valeus b[0], b[1], b[2])?

Thanks a lot!

Pere

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# Linear recurrence with polynomial coefficients

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