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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 next is the given number. There are also non-polynomial solutions.

The simplest rule, using an order 3 polynomial, is

Un = (-7n3 + 59n2 - 144n + 118)/2

and, accordingly, the next number is -1.

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