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It is easy to find a rule based on a polynomial of order 6 such that the first six numbers are as listed in the question followed by any chosen number in nth position. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.

The simplest solution, based on a polynomial of order 2, is

T(n) = n^2 - 1 for n = 1, 2, 3, ...

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