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Math Help - Explaination for the 'repertoire method' for solving recurrences/sums?

  1. #1
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    Explaination for the 'repertoire method' for solving recurrences/sums?

    Repertoire method to solve summation, where in you express the sum as a function of some constant times some function of n, like A(n) etc... I am trying to follow 'Concrete Mathematics', by Graham and Knuth, but having some difficulties in understanding these techniques which they applied to solve Josephus problem, could anybody explain please, giving an example....
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    please any replies!
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  3. #3
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    Perhaps my question was not exact..
    here is a problem.

    Solve the recurrence
    Q_0 = \alpha;
    Q_1 = \beta;
    Q_n = (1 + Q_ {n-1}\ )/Q_ {n-2} , for n \geq 1.

    Assume that Q_n \ != 0 for all n \geq 0.

    How do you do this, specifically I need to do this usuing 'repertoire method', that is assuming
    Q_n = A(n)\alpha + B(n)\beta + C(n) \gamma
    Although what equation I wrote above may not be right, since I don't understand such assumption, amd thus I need help....
    Please...
    Last edited by natarajchakraborty; September 17th 2008 at 07:41 AM.
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  4. #4
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    Quote Originally Posted by natarajchakraborty View Post
    Perhaps my question was not exact..
    here is a problem.

    Solve the recurrence
    Q_0 = \alpha;
    Q_1 = \beta;
    Q_n = (1 + Q_ {n-1}\ )/Q_ {n-2} , for n \geq 1.

    Assume that Q_n \ != 0 for all n \geq 0.

    How do you do this, specifically I need to do this usuing 'repertoire method', that is assuming
    Q_n = A(n)\alpha + B(n)\beta + C(n) \gamma
    Although what equation I wrote above may not be right, since I don't understand such assumption, amd thus I need help....
    Please...
    /****************/
    The key idea is value of function and constants not matter!
    Only we want to know, how many constants are there.
    If we find this answer we will also know the value of given recurrence.
    Thats it!
    /****************/
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