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Math Help - recurrence relations - degree of the recurrence

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    recurrence relations - degree of the recurrence

    I have a recurrence:

    an = an-1 + an-2 + 2n-3

    is this a degree of 2 or 3?

    b/c if it's 2 I get
    r2 r 1 & there are no integer roots....

    but if it's degree 3, it would be r^3 - r^2 - r - 2 & I don't know how to find the roots of a degree 3 function...
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by amyu2005 View Post
    I have a recurrence:

    an = an-1 + an-2 + 2n-3

    is this a degree of 2 or 3?

    b/c if it's 2 I get
    r2 r 1 & there are no integer roots....

    but if it's degree 3, it would be r^3 - r^2 - r - 2 & I don't know how to find the roots of a degree 3 function...
    don't know much about difference equations but assuming your cubic is correct, we apply the rational roots theorem and see that r = 2 is a root. and so (r - 2) is a factor. after factoring this out, with the aid of polynomial long division, or synthetic division, or your favorite method, we get (r - 2)(r^2 + r + 1)
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