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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 polynomial of order 4 is:

Un = (-5n5 + 58n3 - 232n2 + 371n - 186)/6 for n = 1, 2, 3, ...

and accordingly, the next number is -44.

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11y ago

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