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Math Help - Nonlinear recurrence relation

  1. #1
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    Nonlinear recurrence relation

    Is it possible to find a closed form to a single variable sequence with a multivariable recurrence relation?

    For example, define f:\mathbb{N}\times\mathbb{N} \to \mathbb{N} by f(i,j) = \frac{2^{i-1}(6j-5+4[i]_2)+1}{3} where [i]_2 = 0 if i is even and [i]_2 = 1 if i is odd. Note: f is a bijection. Next, let a_n be a sequence with the following recurrence relations:

    a_{4n-1} = 4a_n + 1

    and the extremely nonlinear relation:

    a_{f(i,j+1)} = 64a_{f(i,j)}+7(2^i+3)

    For this question, assume that \min{\mathbb{N}} = 1 and a_1 through a_i are known where they are the minimum number of elements needed to start the recursion.
    Last edited by SlipEternal; September 1st 2012 at 08:33 PM.
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  2. #2
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    Re: Nonlinear recurrence relation

    A solution has been found for this problem that does not involve convoluted sequences. Thanks to anyone who consider it, for however briefly they did.
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