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The answer depends on where, in the sequence, the missing number is meant to go.

Furthermore, whatever number you choose and wherever in the sequence it is meant to be, it is always possible to find a polynomial of degree 5 that will go through all five points given in the question and your chosen one.

Using a polynomial of degree 4, the next number is 213.

The rule is

Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, 3, ...

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