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Given any number it is easy to find a rule based on a polynomial of order 4 such that the four numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.

The polynomial with the lowest order for this sequence is

Un = -3n2 + 14n + 64 for n = 1, 2, 3, ...

and, accordingly, the next number is 59.

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