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Find Kernels of Linear Recurrences
Find the coefficients for a linear constant coefficient recurrence satisfied by a list of numbers.
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kernel = FindLinearRecurrence[Table[Fibonacci[k]^3 , {k, 10}]]
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r1 = LinearRecurrence[kernel, Table[Fibonacci[k]^3 , {k, 4}], 15]
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r2 = Table[Fibonacci[k]^3 , {k, 15}]
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r1 - r2
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r3 = RecurrenceTable[{y[k + 4] == 

    3 y[k + 3] + 6 y[k + 2] - 3 y[k + 1] - y[k], 

   y[1] == Fibonacci[1]^3, y[2] == Fibonacci[2]^3, 

   y[3] == Fibonacci[3]^3, y[4] == Fibonacci[4]^3}, y, {k, 15}]
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r3 - r2
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