## generalized binet formula for linear recurrent sequences [closed]

Hi all I google about but still nothing my question is this. Considering a linear recurrent sequence where the n+i term is the linear sum of the previous k terms is there something like a Binet Formulas to express the n+1 term as power of the previous k terms?

Thank is someone could help

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Voting to close as too localized. See mathoverflow.net/faq#whatquestions – Ricky Demer Aug 19 2011 at 9:12
too localized? I'd agree on "not a real question" (because incomprehensible). – darij grinberg Aug 19 2011 at 10:12
But I'd like pgiacome to make the question clearer. Note: the Binet formulas don't "express the n+1 term as power of the previous k terms". – darij grinberg Aug 19 2011 at 10:13
Not really a research level question, it's an exercise using Jordan normal form, so voting to close. Try stackexchange. And as Darij said, the n′th term isn't a power of previous terms. What happens is that the n'th term of the sequence has the form $$\sum_{i=1}^k P_i(n)\alpha_i^n$$, where the $P_i(n)$ are polynomials in $n$. – Joe Silverman Aug 19 2011 at 11:52
pgiacome, as Joe Silverman said, and as the faq says, this site is for questions of interest to research mathematicians, not questions covered in introductory textbooks on discrete mathematics. Your question will get a better reception at math.stackexchange, especially if you take some care to phrase it a little better. – Gerry Myerson Aug 19 2011 at 12:42
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