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Given any number it is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.
The simplest solution, using a polynomial of order 6, is
Un = -0.0069n6 + 0.1708n5 - 1.6319n4 + 7.6458n3 - 18.3611n2 + 23.1833n - 10 for n = 1, 2, 3, ...
Accordingly, the next term is 11.
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