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Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the sixth is the given number. That is, it is easy to find a rule so that any number can be the "next" in the sequence.
The simplest rule based on a polynomial of order 4 is
Un = (-7n4 + 80n3 - 314n2 + 499n - 246)/6 for n = 1, 2, 3, ...
and according to this rule, U6 = -58.
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