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There are infinitely many polynomials of order 4 that will give these as the first four numbers and any one of these could be "the" explicit formula.

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,

t(n) = (-17*n^4 + 170*n^3 - 575*n^2 + 830*n - 400)/4 for n = 1, 2, 3, ...

The Simplest, though is

t(n) = 5*n^2 - 5*n + 2 for n = 1, 2, 3, ...

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Q: How do you find the explicit formula to the sequence 2 12 32 62?
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