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Any number that you choose can be the nth number. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by the chosen number in the 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.
For example, U(n) = (3*n^4 - 30*n^3 + 105*n^2 - 126*n - 120)/4 gives the next number as 0orU(n) = (19*n^4 - 190*n^3 + 665*n^2 - 806*n - 696)/24 gives the next number as 1and so on.
The simplest solution, though, based on a polynomial of order 3 is U(n) = 6*(x - 8)


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