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There are infinitely many pattern rules. 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 any number that you choose to be the next one. 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 3 is

t(n) = 1.5*(-n^3 + 12n^2 - 26n + 21) for n = 1, 2, 3, ...

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10y ago
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Q: What is the pattern rule for 4 6 16 30?
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